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ESSENTIALS  OF 
ARITHMETIC 

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THE  LIBRARY 

OF 

THE  UNIVERSITY 

OF  CALIFORNIA 

LOS  ANGELES 


.OS  ANGELES 

-   •^l.  SCHOOL 


STATE  NORMAL  SCHOOL 


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WENTWORTH-SMITH  MATHEMATICAL  SERIES 

ESSENTIALS  OF 
ARITHMETIC 

PKIMAEY  BOOK 

BY 

GEORGE  WENTWORTH 

AND 

DAVID  EUGENE  SMITH 


A= 


^a  SMITH 


♦ 


^ 


GINN  AND  COMPANY 

BOSTON  •  NEW  YORK  •  CHICAGO  •  LONDON 
ATLANTA  •  DALLAS  •  COLUMBUS  •  SAN  FRANCISCO 


COPYRIGHT,  1915,  BY  GEORGE  WENTAVORTH 

AND   DAVID   EUGENE  SMITH 

ALL  RIGHTS  RESERVED 

615.8 


1 


GINN  AND  COMPANY-  PRO- 
FRIETORS  •  BOSTON  •  U.S.A 


103 
PEEFACE 


This  book  is  the  first  of  a  series  of  three  intended  to  cover  the 
essentials  of  arithmetic  in  the  eight  school  years  of  the  elementary 
course.  It  consists  of  five  chapters,  the  first  of  which  reviews  the 
work  usually  done  in  the  first  and  second  grades,  the  others  covering 
the  work  of  the  successive  half  grades  through  the  fourth  school  year. 
If  it  is  introduced  in  Grade  II,  the  pupils  should  complete  Chapter  I 
in  that  year;  but  if  it  is  first  placed  in  the  hands  of  the  class  in 
Grade  III,  it  will  suffice  to  take  a  rapid  review  of  Chapter  I,  omitting 
such  portions  as  may  already  be  perfectly  familiar  to  the  children. 

A  textbook  for  these  grades  can  be  constructed  on  any  one  of 
several  definite  plans,  or,  indeed,  with  little  attention  to  any  system- 
atic arrangement  whatever.  It  may  consist  of  a  series  of  devices  for 
teachers,  such  as  games  and  dramatizations,  all  valuable  in  them- 
selves but  not  offering  the  material  needed  in  a  usable  textbook. 
To  be  usable  a  book  should  suggest  devices  of  this  kind,  which  with 
many  others  the  teachers  may  bring  into  their  work,  but  it  fails  of 
its  purpose  if  it  uses  most  of  its  limited  space  in  this  manner.  The 
primary  purpose  of  a  textbook  in  arithmetic  is  to  furnish  a  large 
amount  of  material  which  the  teachers  would  otherwise  have  to  dic- 
tate, and  to  arrange  this  material  in  a  systematic  order.  Teachers 
need  hundreds  of  examples  in  addition,  hundreds  of  examples  in 
subtraction,  and  so  on,  and  they  should  not  be  required  to  make  up, 
arrange,  and  dictate  this  material.  Teachers  always  welcome  sugges- 
tions of  games,  of  dramatizations  of  number  relations,  and  of  means 
to  apply  number  facts  to  the  daily  experiences  of  the  child,  but 
such  devices  of  teaching  must  necessarily  come  in  large  part  from 
the  teachers  themselves. 


iv  PEEFACE 

This  book  stands,  in  the  first  place,  for  good,  well-arranged  mathe- 
matics, and  not  for  the  scrappy  presentation  which  always  fails  to 
give  to  the  pupil  that  feeling  of  mastery  of  the  subject- to  which  he 
is  entitled ;  and  in  the  second  place  it  appeals  to  the  pupil's  human 
interests  by  relating  the  subject  to  his  personal  needs  and  to  the 
life  in  which  he  finds  himself.  It  seeks  to  balance  reasonably  these 
two  features,  refraining  on  the  one  hand  from  devoting  all  its  space 
to  abstract  drill,  and  on  the  other  hand  from  failing,  through  the 
sacrifice  of  its  space  to  methods  of  teaching,  to  give  the  amount  Of 
drill  that  is  necessary.  It  recognizes  that  the  children  who  study 
its  pages  have  already  been  in  school  from  one  to  two  years,  that 
they  not  only  possess  a  fair  knowledge  of  number  but  that  motives 
for  study  have  already  begun  to  be  formed,  and  that  the  kindergarten 
stage  is  already  passing  out  of  their  lives.  Devices  that  are  needed 
in  Grade  I  are  not  necessary  in  Grade  III;  and  the  teachers,  to  a 
large  extent,  must  be  the  judges  as  to  how  long  they  shall  keep  to 
the  concrete  introduction  to  the  work,  and  as  to  the  use  they  shall 
make  of  the  numerous  devices  suggested  in  the  book. 

It  is  the  hope  of  the  authors  that  teachers  will  find  that  the  series 
furnishes  exactly  the  essentials  for  good  arithmetic  work  in  the 
elementary  schools  and  presents  these  essentials  in  the  most  usable 

manner. 

GEORGE  WENTWORTH 
DAVID  EUGENE  SMITH 


CONTENTS 

CHAPTER  I 

PAGE 

I.    Counting  to  Twelve 1 

II.   Addition 5 

III,  Addition  and  Subtraction 10 

IV.  Counting  to  100 15 

V.    Addition 20 

VI.    Subtraction 32 

VII.    Using  what  you  have  Learned 36 

VIII.   Fractions 38 

IX.    Measures 44 

X.    Review  Drill 47 

XI.    Using  what  you  have  Learned 49 

XII.   Little  Examinations    . 62 

CHAPTER  II 

I.   Numbers  to  1000 58 

II.   Addition 57 

III.  Subtraction 64 

IV.  Multiplication  and  Division  Tables 71 

V.    Multiplication 85 

VI.   Using  what  you  have  Learned 90 

VII.   Division 93 

VIII.   Fractions 97 

IX.    General  Review 102 

X.   Using  what  you  have  Learned 104 

XI.   Little  Examinations 108 

CHAPTER  III 

I.   Reading  and  Writing  Numbers 109 

II.    Addition 114 

III.    Subtraction 120 

V 


vi  CONTENTS 

PAGE 

IV.  MnLTIPLICATIOK  AND  DIVISION 124 

V.  Using  what  you  have  Learned 145 

VI.  Fractions 147 

VII.  Measures 149 

VIII.  Review 153 

IX.  Using  what  you  have  Learned 164 

X.  Little  Examinations 166 

CHAPTER  IV 

I.  Reading  and  Writing  Numbers 167 

II.  Addition 169 

III.  Subtraction 170 

IV.  Multiplication 172 

V.  Using  what  you  have  Learned 183 

VI.  Division 187 

VII.  Fractions 200 

VIII.  Measures 213 

IX.  Review 218 

X.  Using  what  you  have  Learned 220 

XI.  Little  Examinations 222 

CHAPTER  V 

I.  Reading  and  Writing  Numbers     .    .    .    .  ' 223 

II.  Addition 225 

III.  Subtraction 226 

IV.  Multiplication 227 

V.  Division 230 

VI.  Measures 233 

VII.  Using  what  you  have  Learned 246 

VIII.  Fractions 248 

IX.  Aliquot  Parts 258 

X.  Bills  and  Receipts 260 

XI.  General  Review 264 

XII.  Using  what  you  have  Learned 269 

XIII.  Little  Examinations 272 

XIV.  What  THE  Pupil  should  Know  when  HE  HAS  Finished  THIS  Book  273 

Tables  for  Reference 279 

Index 281 


ESSENTIALS  OF  ARITHMETIC 

PRIMARY  BOOK 

CHAPTER  I 
I.   COUNTING  TO  TWELVE 

What  You  may  have  Learned.  You  have  learned  to  count 
and  to  write  numbers.    Can  you  count  to  ten  ? 

Are  there  twenty  children  in  this  room  ? 

Can  you  tell  how  many  children  there  are  in  this  room  ? 

Do  you  know  what  I  mean  when  I  speak  of  haK  the 
children  in  the  room? 

Do  you  know  how  many  cents  there  are  in  a  dollar  and 
a  quarter,  or  a  dollar  and  a  half  ? 

If  your  father  has  a  dollar  and  spends  seventy-five  cents 
for  you,  do  you  know  how  much  he  will  have  left  ?  If  you 
cannot  tell  now,  you  will  be  able  to  tell  after  you  have 
studied  this  book. 

This  page  calls  attention  to  some  things  that  the  children  know,  and 
to  some  that  they  have  still  to  learn.  The  teacher  will  find  it  of  advantage 
to  suggest  from  time  to  time,  in  simple  problems,  the  motives  which  should 
prompt  the  pupil  to  study  further.  The  reading  of  some  of  the  problems 
a  few  pages  in  advance  is  often  a  good  stimulus  for  work. 

Notes  in  this  type  throughout  the  book  are  intended  for  the  teacher. 

1 


COUNTESTG  TO  TWELVE 


ORAL  EXERCISE 

1.  Here  are  some  children  playing  with  their  pet 
donkey.    How   many   children   do   you   see? 

2.  How  many  children  are  riding  on  the  donkey  ? 

3.  How  many  girls  are  riding  on  the  donkey  ? 

4.  How  many  boys  are  riding  on  the  donkey  ? 

5.  How  many  children  are  on  the  ground  ? 

6.  If  the  little  girl  without  a  hat  should  get  off,  how 
many  children  would  be  left  on  the  donkey  ?  How  many 
girls  would  be  left  on  the  donkey? 

7.  If  both  Httle  girls  should  get  off,  how  many  children 
would  be  left  on  the  donkey  ? 

Teachers  should  always  be  sure  that  new  words  do  not  obscure  the 
meaning.  Since  this  book  is  not  intended  for  Grade  I,  the  above  words 
are  probably  all  known,  otherwise  they  should  be  explained. 


PLAYING  STORE  8 

ORAL  EXERCISE 

1.  Let  us  play  store.    How  many  are  there  to  play? 

2.  How  many  clerks  shall  we  have  in  the  store  ? 

3.  How  much  shall  we  charge  for  apples  ? 

4.  How  many  apples  do  you  wish  to  buy  ? 

5.  How  much  shall  we  charge  for  oranges  ? 

6.  How  many  oranges  do  you  wish  to  buy  ? 

7.  How  many  bottles  of  milk  are  Q    fl  and  Q    fl    fl  ? 

8.  Jack   sells    some    blocks    for   building   playhouses. 
How  many  blocks  are  g  g  g  and  0  0? 

9.  Rob  sells  some  dolls.    He  sells  5  dolls  to  Mary  and 
1  doll  to  Kate.    How  many  dolls  does  he  sell  ? 

10.  Kate  buys  some  cups  for  the  doll's  table.  How 
many  cups  are  ^  ^Q  ^Q  and  ^  "^  ? 

11.  Kate  buys  an  orange  for  3  cents.  She  gives  5  cents. 
How  much  change  does  she  get  ? 

This  shows  what  is  called  the  dramatization  of  arithmetic  — acting  out 
a  real  situation.  Such  work  is  more  real  when  planned  and  suggested  by 
the  teacher  than  when  it  is  given  in  a  textbook.  On  this  account  only  a 
limited  amount  of  space  can  profitably  be  given  to  the  subject  in  a  book 
of  this  kind.    Frequent  suggestions  are  made,  however. 

Among  the  common  rhymes  that  can  be  dramatized  at  this  time  are 
the  following  :  Bo-peep,  Going  to  St.  Ives,  Old  Mother  Hubbard,  Ten  Little 
Indians,  Three  Little  Kittens,  and  the  Old  Woman  who  lived  in  a  Shoe. 
Among  the  common  stories  are  Jack  and  the  Beanstalk,  the  Three  Bears, 
and  Jack  the  Giant  Killer.  Among  the  dramatized  occupations  are  run- 
ning a  grocery  store,  building  a  snow  fort,  hunting  eggs,  picking  or  selling 
fruit,  sewing,  being  a  trolley-car  conductor,  and  fishing. 


4  COUNTING  TO  TWELVE 

WRITTEN  EXERCISE 

1.  Write  in  figures  the  numbers  from  1  to  5. 

2.  Write  in  figures  the  numbers  from  5  to  10,  and  then 
from  10  back  to  5. 

3.  Write  in  figures  the  numbers  from  7  to  12,  and  then 
from  12  back  to  7. 

4.  Write  in  figures  the  numbers  from  9  back  to  2,  and 
then  up  from  2  to  9. 

5.  Write  in  figures  the  numbers  from  12  back  to  1, 
and  then  up  from  1  to  12. 

6.  Write  in  figures  the  number  of  words  in  this  line. 

7.  Close  your  eyes  and  hear  me  tap  the  desk.    Write 
in  figures  the  number  of  taps  you  heard. 

8.  Close  your  eyes  and  touch  the  fingers  which  I  hold 
out.    Write  in  figures  the  number  of  fingers  you  touched. 

9.  Write  in  figures  the  nmnbers  from  0  to  10. 

10.  Write  in  figures  the  numbers  from  10  back  to  0. 

11.  Write  in  figures  the  number  of  doors  in  this  room, 
and  then  write  the  number  of  windows. 

12.  Write  in  figures  the  number  of  desks  in  your  row. 

13.  Write  in  figures  the  numbers  which  come  just  after 
3,  9,  5,  7,  1,  and  8,  in  counting  from  0  to  12. 

14.  Write  in  figures  the  numbers  which  come  just  before 
7,  6,  9,  5,  3,  and  10,  in  counting. 

15.  Write  in  figures  the  number  which  comes  between 
9  and  11  in  coimting. 


ADDITION 

II.   ADDITION 
ORAL  EXERCISE 

1.  How  much  do  you  add  to  2  cents  to  make  3  cents? 

2.  How  many  marbles  are  2  marbles  and  2  marbles  ? 

3.  How  many  boys  are  5  boys  and  2  boys  ? 

4.  How  many  blocks  are  7  blocks  and  2  blocks  ? 


Addition.  When  we  add  3  cents  and  4  cents  we  get  7  cents, 
and  7  cents  is  called  the  sum  of  3  cents  and  4  cents. 

We  write  the  numbers  to  be  added,  one  above 
the  other,  with  a  bar  below  the  lower  one,  and 
the  sum  below  the  bar. 

The  sum  of  3  and  4  is  also  written  3  +  4  =  7. 


The  sign  +  means  and.  This  sign  is  also  called  plus.  The 
sign  =  means  equals. 


State  rapidly 

these 

sums 

• 

5.  2         4 
1         1 

8 
1 

6 
1 

9 
1 

1 
1 

5 
1 

7 
1 

3 
1 

10 
1 

6.  5         3 

2        2 

8 

2 

1 

2 

6 

2 

4 

2 

9 
2 

2 

2 

7 
2 

10 
2 

The  teacher  will  find  sets  of  cards,  each  having  a  combination  like 
those  in  Ex.  5,  useful  for  drill,  the  set  to  be  enlarged  as  the  class  advances. 

Less  written  than  oral  work  should  be  given  at  first,  and  pupils  should 
be  required  to  do  the  written  as  well  as  the  oral  work  quickly.  Loitering 
brings  both  inaccuracy  and  lack  of  interest. 


ADDITION 


DEVELOPMENT  GAME 

1.  These  girls  count  2  for  each  skip  of  the  rope.    They 
count  "  2,  4,  6,"  and  so  on.    Count  for  four  skips. 

2.  Count  2  for  each  skip  of  the  rope  to  five  skips. 

3.  Count  2  for  each  skip  of  the  rope  to  six  skips. 

4.  The  girls  swing  the  rope  faster.    Now  they  count 
3  for  each  skip.     Count  for  three  skips. 

5.  Count  3  for  each  skip  to  four  skips. 

6.  Ruth  cannot  jump  very  well,  but  she  can  add  fast. 
Count  4  for  each  of  her  skips  for  three  skips. 

7.  Count  by  2's  from  2  to  12. 

8.  Count  by  3's  from  3  to  12. 

9.  Count  by  4's  from  4  to  12. 

10.  Count  backwards  by  2's  from  12  to  2. 

From  time  to  time  a  certain  amount  of  dramatized  work  should  be 
introduced  by  the  teacher,  as  suggested  on  page  3,  but  it  should  not  be 
so  extravagantly  used  as  to  leave  no  time  for  real  number  work. 


DRILL  WORK 
ORAL  EXERCISE 

State  rapidly  these  sums : 

1.  5        3         7        1        4        6 
3        3        3        3        3        3 


2.  3 

1 

4 

6 

2 

7 

5 

8 

0 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

0 

3.  4 

2 

1 

5 

3 

7 

6 

0 

4 

3 

5 

5 

5 

5 

5 

5 

5 

5 

1 

2 

4.   1 

3 

2 

5 

6 

0 

4 

6 

5 

4 

6 

6 

6 

6 

6 

6 

6 

0 

1 

2 

5.  2 

1 

4 

3 

0 

5 

2 

1 

4 

3 

7 

7 

7 

7 

7 

7 

8 

8 

8 

8 

6.  0 

8 

0 

2 

1 

3 

9 

8 

7 

7 

8 

0 

9 

9 

9 

9 

0 

1 

1 

2 

WRITTEN  EXERCISE 


it/a^e  pictures  like  this,  showing  the  sums 
helow.    Write  the  answers. 


•        •  • 

•    e    • 


3  +  4=  7 

2  +  5 

6  +  0 

4  +  2 

5  +  3 

5  +  5 

6  +  2 

2  +  8 

4  +  3 

8  +  4 

9  +  2 

3  +  5 

0  +  8 

6  +  5 

7+3 

7+5 

In  drill  work  of  this  kind,  number  games  may  be  used  with  discretion. 
Tor  example,  one  of  these  number  combinations  may  be  placed  on  each 
step  of  a  ladder  drawn  on  the  blackboard,  and  children  may  climb  rapidly 
Tuitil  they  fall  off  by  making  an  error. 


ADDITION 


ORAL  EXERCISE 

1.  How  many  children  are  there  in  the  picture  ? 

2.  How  many  children  are  4  children  and  3  children  ? 

3.  How  many  children  are  5  children  and  2  children  ? 

Add  these  numbers  and  make  problems  about  them : 

4.  6136        771199 
1660217310 


6.  5 

2 


8       0 


WRITTEN  EXERCISE 

Copy  and  add : 

1.  3  +  0         5  +  3  7  +  2  6  +  3  5  +  4 

2.  0  +  3         3  +  5^  2  +  7  3  +  6  6  +  0 

3.  4  +  0  4  +  6  8  +  1  4  +  1  8  +  2 


GAMES 


DRILL  GAMES 

1.  Our  class  played  the  game  of  Numbers  on  the  Hoop. 
The  teacher  put  this  picture  on  the  blackboard.  As  Ruth 
pointed  to  the  numbers  on  the  hoop,  i 

we  added  5  to  each.    Add  5  to  each  of       ^y^      ^\o 
these  numbers : 


1 

3 

2 

7 

0 

6 

5 

4 

7 

0 

6 

4 

2 

5 

3 

1 

Change  the  number  to  be  added  and  write  the 
new  number  in  the  hoop,  making  a  new  game.  ^ 

The  numbers  must  be  chosen  so  that  the  sum,  at  this  time,  does  not 
exceed  12.    Similarly  for  Ex.  2  and  other  games. 

2.  We  played  Running  the  Square.  The  teacher  put 
this  picture  on  the  blackboard.  As  John  pointed  to  the 
numbers  at   the   comers   and   on  the     7  5  8 

sides,  we  ran  around  the  square  with 
him  and  added  2  to  each  number. 
Add  2  to  each  of  these  numbers :  ^ 


2 


3.  We  also  played  Running  the  Triangle.  The  teacher 
put  this  picture  on  the  blackboard,  and  we  tried  to  see  how 
fast  we  could  run,  adding  each  number  to 
the  one  inside.  Run  around,  beginning 
with  4.  Run  around,  beginning  with  9. 
Run  around,  beginning  with  5.  Run 
around,  beginning  with  6.  Run  around, 
beginning  with  8. 


10  ADDITION  AND  SUBTRACTION 

III.   ADDITION  AND  SUBTRACTION 
ORAL  EXERCISE 

1.  There  are  6  children  in  a  row.    How  many  children 
must  be  added  to  this  number  to  make  11  ? 

2.  Jennie  wishes  to  buy  a  5-cent  paper.   She  has  2  cents 
in  her  pocket.   How  many  more  cents  must  she  have  ? 

3.  Jack  has  8  marbles.    How  many  more  marbles  must 
he  get  so  as  to  have  11  marbles  in  all? 

4.  After  we  have  studied  6  pages  of  this  book,  how 
many  more  must  we  study  to  make  10  pages  in  all? 

5.  What  number  must  we  add  to  6  to  make  9  ?  to  3 
to  make  7  ?  to  7  to  make  10  ?  to  10  to  make  12  ? 

6.  What  numbers  must  I  put  in  place  of  the  stars  to 
have  these  additions  all  right  ? 

2365  733  9 

5779113  412 

7.  Answer  these  questions  : 

5  and  what  number  are  7  ? 
7  and  what  number  are  12  ? 

6  and  what  number  are  11  ? 

8.  Name  the  numbers  to  put  in  place  of  these  stars : 

5  +  *=  10  4  +  *  =  6  *  +  6=12 

7  +  *  =  12  6h-*  =  9  6  +  *=  12 

9  +  *  =  11  *-f4  =  6  7  +  *=  11 


SUBTRACTION 


11 


ORAL  EXERCISE 

1.  Helen  is  counting  her  blocks.    She  has  7  blocks  and 
takes  away  3  blocks.   How  many  blocks  are  left? 

2.  If  Helen  takes  4  blocks  from  7  blocks,  how  many 
blocks  are  left? 

3.  How  many  blocks 
are  7  of  these  blocks  less 

3  of  these  blocks  ? 

4.  How  many  blocks 
are  7  of  these  blocks  less 

4  of  these  blocks  ? 

5.  If    Helen    has    7 
cents  and  spends  4  cents,  how  many  cents  has  she  left? 


Subtraction.  Taking  3  blocks  from  7  blocks  is  called 
subtraction.    We  subtract  3  blocks  from  7  blocks. 

To  show  that  we  subtract  3  from  7  we  write  the  work 
in  a  column  as  shown  below  in  the  margin.  We  may  also 
show  it  by  writing  the  numbers  like  this : 

7-3  =  4, 
which  we  read  in  any  one  of  these  three  ways : 

7  less  3  is  4, 

7  minus  3  equals  4, 
or  3  from  7  is  4. 

The  pupil  is  now  old  enough  to  understand  all  these  expressions,  and 
he  should  use  them  interchangeably.  The  relation  of  3  +  4=7  to  7  —  4  =  3 
and  7  —  3  =  4  should  be  understood  by  .the  pupil. 


12 


ADDITION  AND  SUBTEACTION 


ORAL  EXERCISE 

1.  Jennie  is  bu3dng  apples  from  Kate.  If  she  buys  2 
cents'  worth,  and  gives  Kate  10  cents,  how  much  change 
should  she  get? 

2.  If  she  buys  5  cents'  worth  of  candy,  how  much 
change  should  she  get  if  she  gives  Kate  10  cents? 

3.  How  much  money 
should  she  pay  Kate 
for  2  pop-corn  balls  if 
they  cost  2  cents  each  ? 
What  change  should 
she  get  if  she  gives 
Kate  a  5-cent  piece. 

4.  If  Jennie  buys  3 
apples,  paying  1  cent 
for  each,  and  a  pop-corn 
ball  for  2  cents,  how  much  does  she  pay  for  all  ? 

5.  If  Jennie  buys  2  apples  at  1  cent  each,  and  5  cents' 
worth  of  candy,  and  4  cents'  worth  of  pop-corn  baUs,  how 
much  does  she  pay  for  all  ? 


WRITTEN  EXERCISE 

Copy  and  suhtract : 


1.  6 
4 

8 
5 

6 

2 

7 
1 

3 
1 

4 
2 

6 
3 

2.  9 

7 

6 
0 

6 
1 

8 
3 

11 
9 

12 
3 

12 

2 

GAMES 


13 


DEVELOPMENT  GAME 

1.  In  school  to-day 
we  played  the  game  of 
Climbing  the  Ladder. 
We  chmbed  as  fast  as 
we  could.  When  any 
one  made  a  mistake 
he  fell  ofe.  Chmb  the 
ladder  in  the  picture. 
These  numbers  are 
5-2,  4-2,  3-2, 
8-2,  9-2,  7-2, 
and  6-2.  Tell  the 
answers  as  fast  as 
you  can. 

2.  Tell  the  answers 
for  9-2,  7-2,  5-2. 

Climb  these  ladders  as  fast  as  you  can,  heginning  at  the  foot. 


3. 

4. 

5. 

6. 

12-3 

12-4 

10-5 

11-6 

10-3 

10-4 

12-5 

10-6 

5-3 

11-4 

11-5 

12-6 

3-3 

7-4 

7-5 

7-6 

8-3 

5-4 

5-5 

6-6 

4-3 

9-4 

9-5 

8-6 

9-3 

6-4 

8-5 

9-6 

14  ADDITIOJf  AXD  SUBTRACTION 


ORAL  EXERCISE 

Subtract  re 

ipidly: 

1.  4        6 

3 

8 

3 

7 

9 

9 

8 

10 

3        2 

3 

2 

1 

3 

3 

0 

3 

3 

a.  2       5 

7 

5 

6 

8 

7 

6 

9 

11 

2        1 

2 

3 

3 

5 

0 

1 

8 

10 

WRITTEN  EXERCISE 

Copy  and  subtract : 


1.  4 

5 

6 

7 

8 

9 

10 

11 

12 

12 

4 

4 

4 

4 

4 

4 

4 

4 

4 

0 

2.  5 

6 

7 

8 

9 

10 

11 

12 

12 

11 

5 

5 

5 

5 

5 

5 

5 

5 

1 

2 

3.  6 

7 

8 

9 

10 

11 

12 

12 

12 

10 

6 

6 

6 

6 

6 

6 

6 

3 

2 

0 

4.  7 

8 

9 

10 

11 

12 

11 

11 

11 

12 

7 

7 

7 

7 

7 

7 

0 

1 

11 

12 

5.  If  you  have  10  cents  and  spend  4  cents,  how  many 
cents  will  be  left? 

6.  If  you  have   12  apples  and   eat  2  of  them,   how 
many  apples  will  be  left? 

7.  If  you  have  7  roses  and  give  away  5  of  them,  how 
many  will  j-ou  have  left? 

8.  If  8  girls  stand,  and  then  2  of  them  sit  down,  how 
many  are  left  standing? 


COUNTING  TO  100 


15 


IV.  COUNTING  TO  100 


ORAL  EXERCISE 


1.  How  many  books  are  there  in  the  picture?  If  there 
were  10  more,  how  many  would  there  be  ?  What  name  do 
we  give  to  two  lO's  ? 

2.  How  many  blocks  in 
the  black  and  white  pile? 
How  many  lO's  in  this  pile? 

3.  There  are  3  columns 
of    smaller    blocks.     How 
many  blocks  in  each  column?  How  many  in  all?  What 
name  do  we  give  to  3  tens  ? 

4.  There  are  4  bimdles  of  splints  in  the  picture,  10  in 
each  bundle.  How  many  splints  in  all?  What  name  do 
we  give  to  4  tens  ? 

5.  There  are  5  packages  of  envelopes,  10  in  each  pack- 
age. How  many  envelopes  are  there  ?  What  name  do  we 
give  to  5  tens  ? 

6.  Read  these  nmnbers : 

10  20  30  40  50 

60  70  80  90  100 

7.  How  many  tens  are  there  in  20?  in  30?  in  70? 
in  40  ?   in  50  ?   in  90  ?   in  100  ? 

8.  What  name  do  we  give  to  9  tens  ?  to  6  tens?  to  8  tens? 
to  7  tens?  to  10  tens? 

9.  Tell  how  to  write  seventy  on  the  blackboard. 


16  COUNTING  TO  100 

ORAL  EXERCISE 

1.  If  you  call  2  tens  twenty  and  write  it  20,  and  if  you 
call  3  tens  thirty  and  write  it  30,  what  should  you  call 

4  tens,  and  how  should  you  write  it?   Tell  the  same  for 

5  tens,  and  so  on  up  to  10  tens. 

2.  If  ty  in  sixty  means  tens,  then  sixty  means  six  tens. 
Then  what  does  seventy  mean?  What  does  eighty  mean? 

3.  State  rapidly  the  sums : 

2  2  tens         20         30         40         30         40 

3  3  tens         30         40         50         60         20 


United  States  Money.   The  table  of  United  States  money 
isasfoUows:  5  cents  =  1  nickel 

10  cents  =  1  dime 
100  cents  =  1  dollar 

We  write  ^  for  cents,  and  $  for  dollars,  thus : 

25^  means  25  cents, 
and  $10  means  ten  dollars. 


4.  Subtract  rapidly : 

5         5  tens         50         70 

90 

90 

60 

2         2  tens         20         30 

40 

30 

40 

5.  Read  these  numbers : 

10         90        70        20 

50 

$10 

40  (^ 

60        80        30        40 

100 

$30 

70^ 

COUNTING-  TO  TWENTY  17 

ORAL  EXERCISE 

1.  Count  from  1  to  10 ;  then  count  by  tens  from  10  to 
100. 


2.  How  many  splints  are  10  splints  and  1  splint? 

3.  How  many  splints  are  10  splints  and  2  splints  ? 


The  number  after  twelve  is  thirteen.  It  is  written  13, 
which  means  1  ten  and  3  ones. 

The  number  after  thirteen  is  fourteen.  It  is  written  14, 
which  means  1  ten  and  4  ones. 


4.  li  fifteen  means  ^?;e  and  ten,  what  does  sixteen  mean  ? 

5.  Read  these  numbers  and  tell  what  each  means : 
10         14         15         16         30         18         19 

6.  Read  these  numbers  and  tell  what  each  means : 
17  12  10  40  20  13  11 

7.  How  many  pupils'  desks  are  there  in  your  row  of 
desks  ? 

8.  How  many  pupils  are  there  in  your  row  to-day  ? 

9.  How  many  words  are  there  in  Exs.  7  and  8  together  ? 
10.  How  many  boys  are  there  in  your  class  ? 


18 


COUNTING  TO  100 
OKAL  EXERCISE 


1.  Point  to  10  splints  and  3  splints  in  the  picture.  How 
much  is  10  +  3  ?   Write  the  number  on  the  blackboard. 


2.  In  each  group,  how  many  packages  of  10  splints 
each,  and  how  many  splints  over?    Write  the  numbers. 

3.  Read  the  following : 

Twenty  means  2  tens.      Forty  means.  4  tens. 

4.  Read  the  following : 

21  means  20  and  1.  34  means  30  and  4. 

Read  these  numbers : 

5.  21  62  53  84  65  86  77 

6.  31  82  73         .64  75  96  68 

7.  What  number  comes  after  26  in  counting  ? 

8.  What  number  comes  before  35  ? 

9.  What  number  comes  between  47  and  49  ? 

10.  Count  from  20  to  30,  and  then  from  30  back  to  20. 

11.  Count  from  20  to  40,  and  then  from  40  back  to  20. 

12.  Count  from  1  to  50. 

13.  See  if  you  can  count  from  1  to  100,  speaking  the 
words  very  clearly,  in  one  minute.  Maybe  you  can  do  it 
in  less  than  one  minute. 

14.  Count  backwards  from  100  to  90. 


OEDINAL  NUMBERS  19 

ORAL  EXERCISE 

1.  What  grade  do  children  enter  after  the  first  grade  in 
school  ?  What  grade  do  they  next  enter  ? 

2.  If  the  first  day  of  the  week  is  Sunday,  what  is  the 
second  day  of  the  week  ? 

3.  Which  is  the  sixth  day  of  the  week  ? 

4.  What  day  of  the  month  is  to-day  ? 

5.  To-morrow  will  be  what  day  of  the  month  ? 

6.  Yesterday  was  what  day  of  the  month  ? 

7.  Day  after  to-morrow  will  be  what  day  of  the  month  ? 

8.  Which  is  the  first  month  of  the  year  ? 

9.  In  which  month  does  Christmas  come  ?  What  is  the 
number  of  that  month  ? 

10.  What  is  the  number  of  this  page  that  you  are  study- 
ing ?  Then  which  page  of  the  book  is  it  ? 

11.  Which  example  on  this  page  comes  between  the 
seventh  example  and  the  ninth  example? 

WRITTEN  EXERCISE 

1.  Write  the  numbers  from  1  to  10. 

2.  Write  the  names  of  these  numbers : 
79824165 

3.  Write  in  figures  : 

Seven  Three  Four  Nine  Eight 

4.  Write  in  figures  the  first  number  after  5  and  the 
second  number  before  6. 


20  ADDITION 

V.  ADDITION 
ORAL  EXERCISE 

1.  If  you  have  9^  and  earn  4^  more,  how  many  cents 
do  you  then  have  ? 

2.  I  think  of  two  numbers  whose  sum  is  13.    Can  you 
guess  the  numbers  ?    There  are  several  correct  guesses. 

3.  Tell  what  numbers  to  put  in  place  of  these  stars : 
9*8576*8* 

4_9        ^      ^        5_I_1J^_^ 

*  13         *       13         *       13       13       13      13 

4.  If  Carl  is  8  years  old  and  his  brother  is  6  years  older, 
how  old  is  his  brother  ? 

5.  Tell  what  numbers  to  put  in  place  of  these  stars : 
987       10         7*38*- 

5     5      1    A    —    A    Jl    ^    ^ 

*  *         *         ^       14       14       14       14       14 

WRITTEN  EXERCISE 

Copy,  add,  and  make  a  problem  about  each : 

1.  4       8         9         7       10         7         9         6       12 
9546_3758^ 

2.  5       6        5        8      11       11      10      12      10 
87         9         6^_3_5J-_4 

On  this  page  the  work  centers  about  thirteen  and  fourteen  as  sums. 
The  pupil  is  already  familiar  with  sums  to  twelve. 


FIFTEEN  AND  SIXTEEN  AS  SUMS  21 

ORAL  EXERCISE 

1.  If  Frank  earned  9^  on  Monday  and  6^  on  Tuesday, 
how  much  did  he  earn  in  the  two  days? 

2.  If  you  found  7  eggs  in  the  nests  to-day  and  8  eggs 
yesterday,  how  many  have  you  found  in  the  two  days  ? 

3.  Tell  what  numbers  to  put  in  place  of  these  stars : 
98*8'*         6*7* 

^lA^JL^A      —      A 

*  *       15       15       15       15       15       15       15 

4.  Will  is  7  years  old  and  his  sister  is  9  years  older. 
How  old  is  his  sister? 

5.  John  has  8^  and  he  earns  8^  more.     How  many 
cents  has  he  then? 

6.  Tell  what  numbers  to  put  in  place  of  these  stars : 

98**       10         5       12** 
78_9_8_6_*^_3^ 

*  *       16       16         *       16         *       16       16 

WRITTEN  EXERCISE 

Copy,  add,  and  make  a  problem  about  each : 


1.  6 

7 

■7 

9 

10 

11 

13 

14 

15 

9 

8 

9 

6 

_5 

4 

2 

2 

1 

2.  8 

9 

8 

11 

12 

10 

12 

14 

13 

8 

7 

7 

5 

4 

6 

3 

1 

3 

On  this  page  the  work  centers  about  fifteen  and  sixteen  as  sums. 


22  ADDITION 

ORAL  EXERCISE 

1.  If  there  are  9  girls  and  8  boys  in  a  class,  how  many 
pupils  are  there  in  all  ? 

2.  If  Kate's  score  at  bean-bag  is  8  and  Molhe's  is  9, 
what  is  their  total  score?   What  does  "total"  mean? 

3.  Tell  what  numbers  to  put  in  place  of  these  stars : 

9         8         9         8       12'       *         *       15       14 

*         *17       17*17l7l7l7 

4.  Ruth  has  9  boys  and  9  girls  at  her  party.    How  many 
children  are  there  in  all  ? 

5.  Tell  what  numbers  must  be  put  in  place  of  these 
stars,  and  make  a  problem  about  each  example: 

11  +  *=17  *+15=17  8  +  *  =  18 

WRITTEN  EXERCISE 

Copy,  and  add  the  following : 


1.  14 

15 

12 

17 

2 

10 

1 

8 

2 

3 

3 

5 

1 

16 

7 

16 

10 

16 

2.  4 

16 

16 

7 

10 

11 

7 

5 

13 

13 

1 

2 

11 

8 

6 

10 

13 

4 

On  this  page  the  work  centers  about  seventeen  and  eighteen.  The 
pupils  have  now  learned  all  the  combinations  of  two  numbers  whose  sums 
are  eighteen  or  less.  On  the  next  page[  this  work  is  given  in  the  form  of 
tables,  and  the  addition  drill  should  be  accompanied  by  subtraction  drill. 
Drill  also  on  adding  and  subtracting  zero  and  one. 


TABLE  28 


AD 

DITIO] 

5f  TABLE 

1+2  = 

3 

1  +  3  = 

:   4 

1  +  4  = 

:   5 

1  +  5  = 

=  6 

2  +  2  = 

4 

2  +  3  = 

:   5 

2  +  4  = 

:   6 

2  +  5  = 

:   7 

3  +  2  = 

5 

3  +  3  = 

6 

3  +  4  = 

:   7 

3  +  5  = 

=  8 

4  +  2  = 

6 

4  +  3  = 

7 

4  +  4  = 

8 

4  +  5  = 

:   9 

5  +  2  = 

7 

5  +  3  = 

:   8 

5  +  4  = 

■    9 

5  +  5  = 

10 

6  +  2  = 

8 

6+3  = 

9 

6  +  4  = 

10 

6  +  5  = 

11 

7  +  2  = 

9 

7  +  3  = 

10 

7  +  4  = 

11 

7  +  5  = 

12 

8  +  2  = 

10 

8  +  3  = 

11 

8  +  4  = 

12 

8  +  5  = 

13 

9  +  2  = 

11 

9  +  3  = 

12 

9  +  4  = 

13 

9  +  5  = 

14 

10  +  2  = 

12 

10  +  3  = 

13 

10  +  4  = 

14 

10  +  5  = 

15 

1  +  6  = 

7 

1  +  7  = 

8 

1  +  8  = 

9 

1  +  9  = 

10 

2  +  6  = 

8 

2  +  7  = 

9 

2  +  8  = 

10 

2  +  9  = 

11 

3  +  6  = 

9 

3  +  7  = 

10 

3  +  8  = 

11 

3  +  9  = 

12 

4  +  6  = 

10 

4  +  7  = 

11 

4  +  8  = 

12 

4  +  9  = 

13 

5  +  6  = 

11 

5  +  7  = 

12 

5  +  8  = 

13 

5  +  9  = 

14 

6  +  6  = 

12 

6  +  7  = 

13 

6  +  8  = 

14 

6  +  9  = 

15 

7  +  6  = 

13 

•  7  +  7  = 

14 

7  +  8  = 

15 

7  +  9  = 

16 

8  +  6  = 

14 

8  +  7  = 

15 

8  +  8  = 

16 

8  +  9  = 

17 

9  +  6  = 

15 

9  +  7  = 

16 

9  +  8  = 

17 

9  +  9  = 

18 

10  +  6  =  16       10  +  7  =  17       10  +  8  =  18       10  +  9  =  19 

The  pupil  is  already  familiar  with  these  number  facts.  There  is,  how- 
ever, an  advantage  in  reciting  a  table,  as  well  as  in  being  drilled  upon  the 
number  combinations  selected  at  random.  The  latter  drill  is  provided  on 
the  next  page  and  in  the  frequent  reviews. 


24  ADDITION 

ORAL  EXERCISE 

Add  the  following : 

1.  9504320653 
5627153673 


2.   8 

6 

4 

7 

7 

5 

5 

3 

8 

2 

6 

7 

4 

7 

6 

8 

9 

4 

1 

0 

3.   5 

6 

7 

4 

6 

1 

2 

7 

2 

0 

1 

5 

0 

9 

9 

2 

4 

9 

3 

9 

4.  3 

8 

0 

4 

9 

8 

1 

3 

2 

0 

0 

9 

5 

1 

9 

0 

3 

5 

1 

0 

5.  5 

8 

2 

9 

1 

1 

0 

9 

6 

3 

0 

8 

2 

6 

4 

5 

6 

8 

0 

9 

6.  5 

7 

3 

0 

1 

9 

1 

6 

2 

7 

4 

8 

6 

7 

1 

7 

6 

4 

7 

1 

7.  3 

8 

9 

0 

6 

8 

7 

7 

4 

2 

2 

5 

3 

4 

8 

3 

5 

4 

2 

8 

8.  4 

9 

5 

4 

6 

0 

2 

5 

4 

3 

0 

0 

5 

6 

2 

8 

6 

2 

3 

7 

9.  1 

6 

7 

7 

8 

1 

5 

4 

8 

2 

0 

1 

3 

2 

4 

7 

3 

5 

7 

9 

10.  9 

9 

4 

0 

6 

1 

8 

1 

9 

3 

2 

4 

8 

1 

3 

9 

2 

8 

1 

8 

All  the  fundamental  combinations  in  addition  are  given  on  this  page, 
and  hence  the  page  should  be  reviewed  frequently. 


TROUBLESOME  GROUPS  25 

ORAL  EXERCISE 

1.  Which  mimber  do  you  find  easiest  to  add  to  another 
number  ?   Give  four  examples. 

2.  Which  number  do  you  find  hardest  to  add  to  another 
number  ?   Give  four  examples. 

3.  Which  two  numbers  of  one  figure  each  do  you  find 
hardest  to  add? 

The  answers  to  these  questions  will  reveal  the  "  troublesome  "  groups, 
and  these  should  receive  attention  until  they  are  as  familiar  as  the  "  easy  " 
groups.  In  general  the  combinations  given  below  are  the  ones  that  trouble 
children  most.  It  will  be  noticed  that  the  most  difficult  combinations  are 
repeated  several  times. 


Add 

the  following . 

; 

4.  8 

6 

5 

5 

7 

8 

7 

7 

5 

8 

7 

8 

6 

•      5 

5.  7 

6 

8 

8 

8 

7 

3 

5 

8 

5 

7 

4 

8 

8 

6.  5 

8 

8 

5 

8 

6 

5 

7 

8 

7 

8 

6 

7  . 

6 

7.  4 

8 

6 

6 

8  • 

6 

7 

7 

7 

7 

5 

8 

6 

8 

8.  5 

6 

7 

7 

7 

7 

5 

6 

8 

5 

6 

8 

4 

9 

9.  6 

3 

9 

4 

5 

9 

7 

6 

9 

4 

8 

8 

9 

7 

26 


ADDITION 


DRILL  GAME 

1.  The  game  we 
played  to-day  was 
Nimble  Squirrel.  The 
squirrel  jumped  from 
branch  to  branch 
and  told  the  sums  of 
the  numbers.  When 
he  could  not  give 
the  answers  quickly 
he  fell  off.  Be  the 
nimble  squirrel  and 
tell  these  answers  as 
quickly  as  you  can  : 

7+2   5+6 

6+7   8+9 

4+8   9+7 

Beginning  at  the  bottom  of  each  column,  tell  these  sums  as 
you  jump  from,  branch  to  branch : 


2. 

5  +  2 
3  +  2 

8  +  2 

6  +  2 

9  +  2 

1  +  2 
0  +  2 

2  +  2 


3. 

9  +  3 

6  +  3 

2  +  3 
8  +  3 
4  +  3 

3  +  3 

7  +  3 
1  +  3 


4. 

8  +  4 

6  +  4 

7  +  4 
5  +  4 

9  +  4 

0  +  4 

1  +  4 
4  +  4 


5. 

4  +  6 

8  +  5 

5  +  3 
4  +  2 
7  +  1 
0  +  3 

6  +  9 

9  +  8 


6. 

5  +  8 
7  +  6 
3  +  4 

5  +  5 
3  +  9 
2  +  8 

6  +  5 
9  +  6 


DKILL  WORK  27 

ORAL  EXERCISE 

Add  the  following : 

1.  1  11  21  31  1  11  41  61 

2  2223333 


2.   1 

11 

51 

91 

1 

21 

41 

71 

4 

4 

4 

4 

5 

5 

5 

5 

3.  2 

12 

22 

42 

3 

23 

43 

73 

6 

6 

6 

6 

5 

5 

5 

5 

4.  4 

14 

24 

14 

44 

64 

14 

84 

7 

_7 

7 

8 

8 

8 

9 

9 

Add  each  of  the  numbers  4,  9,  7,  8,  6  to  the  folloicing 
numbers  ;  read  the  results  first  by  columns,  then  by  roivs : 

5.   16  17  18  19  15  "  13  12 

26  37  58  69  45  23  32 

•  56  67  78  39  35  63  72 

76  87  68  79  ...75  ...  83  82 

Drill  means  doing  the  same  thing  over  and  over  again  so  as  to  secure 
mechanical  efficiency,  and  the  problem  is  to  do  this  without  making  the 
work  monotonous.  Observe,  for  instance,  that  in  Ex.  4  the  numbers  4  and 
7  are  added  three  times,  but  always  under  different  conditions. 

WRITTEN  EXERCISE 


Ad 

dihe  folloioing : 

4 

14            7 

17 

7 

7     • 

8 

18 

3 

3            9 

9 

19 

0 

1 

1 

0 

0            0 

0 

0 

29 

9 

9 

28  ADDITION" 

Column  Addition.  In  adding  3,  5,  and  7  we  may  arrange 
the  numbers  in  a  column,  and  begin  with  the  lowest  figure. 
Here  we  have  3  +  5  =  8,  and  8  +  7=15.  We  see 
that  15  is  the  sum,  and  write  it  below  the  hne. 

We  make  sure  that  the  work  is  right  by  add- 
ing from  the  top  down,  thus :  7  +  5  =  12,  and 
12  +  3  =  15.  We  then  say  that  we  have  checked 
the  work,  because  the  two  sums  are  the  same. 


7 

5 

_3 

15 


Teach  the  child  to  read  a  column  as  he  reads  a  word,  as  far  as  this  is 
possible.  As  he  looks  at  this  column  he  should  think,  "  3,  8, 15,"  thinking 
no  other  words. 

ORAL  EXERCISE 


Add  the  following : 
1.  1          4          5 

2  3          2 

3  2          2 

6 
1 
1 

5 
1 
2 

2 
4 
3 

3 
3 
3 

2 
3 
3 

2.  5           4           9 
0           4           0 
4          0          0 

9 
1 
0 

9 
1 
1 

8 
2 
0 

8 
1 
1 

3 
2 
8 

WRITTEN  EXERCISE 

Add  the  following  : 


1.  4 

4 

9 

6 

7 

9 

4 

5 

2 

8 

8 

6 

6 

4 

3 

7 

3 

2 

2 

4 

4 

6 

7 

3 

2.  2 

7 

9 

7 

7 

6 

9 

1 

5 

4 

1 

9 

3 

2 

1 

8 

5 

6 

9 

1 

6 

4 

3 

8 

GAMES 


2& 


DRILL  GAME 

1.  To-day  we  played  the  game  of  Number  Sprinters.  If 
a  boy  did  not  give  the  right  answer  when  he  touched  a. 
post,  he  was  out  of  the  game. 

See  how  much  of  a  number  sprinter  you  are,  by  telHng 
the  sums  in  the  picture  as  fast  as  you  can. 

Run  over  these  courses,  and  time  yourself  for  each  course  : 


1 

3 

3 

2 

2 

2 

3 

4 

1 

3 

2 

2 

2 

2 

3 

4 

4 

4 

2 

1 

5 

1 

2 

4 

4 

4 

4 

4 

9 

5 

3 

3 

2 

2 

4 

4 

4 

5 

5 

5 

2 

3 

2 

4 

3 

4 

5 

4 

5 

3 

5 

5 

5 

5 

5 

5 

5 

6 

5 

7 

3 

3 

3 

5 

6 

3 

1 

1 

1 

3 

3 

4 

2 

2 

3 

7 

7 

8 

1 

1 

7 

7 

7 

8 

7 

7 

8 

8 

9 

9 

41 
35 
76 


SO  ADDITION 

Colunin  Addition.  If  you  read  35  pages  of  a  book  on 
Monday  and  41  pages  on  Tuesday,  how  many  pages  did 
you  read  on  both  days  ?  We  see  that  we  must 
add  35  and  41  to  find  the  answer. 

We  write  the  numbers  one  under  the  other, 
ones  under  ones  and  tens  under  tens.  Adding 
the  column  at  the  right  we  have  6 ;  adding  the 
next  column  we  have  7. 

We  first  write  the  6  below  the  line  in  the  ones'  column. 

We  then  write  the  7  below  the  line  in  the  tens'  column. 

The  sum  is  76,  and  so  you  read  76  pages  in  all. 

WRITTEN  EXERCISE 

Add  the  following : 

1.  20  21  21  23  23  24  28 

30  30  35  35  45  52  71 


2.  30 

31 

33 

43 

63 

73 

32 

26 

26 

26 

26 

26 

26 

46 

3.  40 

41 

43 

53 

64 

64 

38 

34 

34 

34 

34 

34 

35 

50 

4.  50 

52 

53 

53 

53 

53 

27 

25 

25 

25 

26 

36 

46 

61 

5.  60 

61 

61 

62 

63 

63 

39 

16 

16 

26 

26 

26 

36 

60 

6.  70 

70 

70 

70 

72 

72  , 

23 

8 

•18 

28 

27 

24 

27  ■ 

46 

GAMES 


REVIEW  GAMES 

1.  Some  children  played  this  number  game.  They  placed 
a  stick  as  shown  in  the  picture,  and  marked  an  oblong  and 
a  circle  on  the  garden 
sidewalk.  They  then 
rolled  balls  toward  the 
stick.  If  a  ball  touches 
the  stick,  it  counts  5 ;  if 
it  stops  in  the  circle,  it 
counts  4  ;  if  it  stops  on 
the  oblong  but  does  not 
touch  the  stick,  it  counts 
3  ;  if  it  stops  anywhere 
else,  it  counts  0.  If  these  were  the  scores,  who  won  the  game? 

John,  5,  4,         4,  3,  0,         3 

Rob,  4,         4,         0,         0,         3,         5 

Frank,         4,  5,  3,  0,  0,  5 

2.  The  janitor  made  this  ladder  for  a  number  game. 
The  children  tried  to  throw  bean- 
bags  through  the  spaces,  each 
space  counting  as  shown  in  the 
picture.  If  a  bag  strikes  the 
ladder,  it  counts  0.  These  were 
three  scores : 

4,    1 

0,    2 
0,   2 

Who  won  the  game  ? 


Kate, 

3,    2,    0,    0, 

Mary, 

1,    1,    3,    2, 

Jennie, 

4,    3,    2,    0, 

32  SUBTRACTION 

VL   SUBTRACTION 
ORAL  EXERCISE 

1.  How  many  cents  must  we  add  to  1^  to  make  3^. 

2.  How  many  tens  must  we  add  to  1  ten  to  make  3  tens  ? 

3.  How  much  must  we  add  to  10  to  make  30  ? 

4.  Name  the  number  which  belongs  where  each  star  is : 
30  +  *  =  50  21  +  *  =  27  32  +  *  =  39 


^  A^     Column  Subtraction.  If  a  book  has  68  pages  and  we  have 
read  21  pages,  how  many  pages  have  we  left  to  read? 

We  see  that  we  must  subtract  21  from  68. 

We  write  the  smaller  number  below  the  larger  number. 
We  first  think  "8  —  1  =  7,"  and  write  the  7  below 
the  line,  under  the  1.  We  then  think  "  6  -  2  =  4," 
and  write  the  4  below  the  line,  under  the  2. 

The  result  is  47,  and  so  we  have  47  pages 
left  to  read. 

To  make  sure  that  the  work  is  correct,  that  is, 
to  check  the  work,  we  add  47  and  21,  the  result  being  68. 

WRITTEN  EXERCISE 


68 
21 

47 


4 


Subtract  the  following  : 

1.     9            90 

60 

50 

55 

75 

86 

7            70 

30 

10 

10 

20 

50 

2.  88            88 

89 

98 

73 

67 

59 

30           31 

42 

16 

41 

36 

27 

DRILL  WORK  83 

ORAL  EXERCISE 

Subtract  the  following : 

1.  9  90  99  96  87  76  86 

3  30  33  32  43  32  36 


2.  7     70     77     78     87 

75 

95 

4     40     44     42     34 

22 

25 

WRITTEN  EXERCISE 

Copy  and  subtract  : 

1.  98     89     93     64     55 

63 

75 

73     46     31     24     21 

52 

25 

2.  82 

78 

65 

53 

31 

29 

67 

50 

37 

52 

12 

11 

18 

47 

3.  68 

79 

84 

86 

73 

81 

39 

11 

21 

30 

22 

22 

30 

7 

4.  68 

76 

69 

96 

74 

77 

48 

23 

40 

24 

42 

40 

25 

3 

5.  73 

94 

74 

77 

95 

78 

66 

31 

50 

51 

33 

61 

34 

20 

^'  6.  If  Frank  has  21  chickens,  how  many  more  must  he 
get  so  as  to  have  34  chickens  in  all  ? 

7.  If  Wilham  has  43  marbles,  how  many  more  must  he 
get  so  as  to  have  55  marbles  in  all  ? 


34  SUBTRACTION 

DRILL  TEST.     ADDING  ONE-FIGURE  NUMBERS 

Add,  and  state  the  ansivers  rapidly : 


1.  1 

0 

7 

6 

2 

8 

9 

7 

3 

9 

1 

2 

1 

2 

1 

2 

1 

2 

1 

2 

2.  0 

7 

.  5 

7 

8 

7 

9 

9 

6 

8 

3 

4 

5 

3 

4 

5 

3 

4 

5 

5 

3.  9 

7 

8 

5 

8 

9 

4 

9 

7 

6 

5 

6 

7 

6 

6 

7 

5 

6 

7 

8 

Such  tests  may  be  used  for  both  oral  and  written  work.  In  the  former 
case  the  results  should  be  stated  rapidly,  with  no  hesitation ;  in  the  latter 
case  the  numbers  should  be  written  neatly,  with  the  answers,  and  a  record 
kept  of  the  time.  The  exercise  should  be  repeated  from  week  to  week  and 
a  comparison  made  of  the  speed  and  accuracy. 


DRILL  TEST.     SUMS  TO  TWENTY 

Add,  and  state  the  answers  rapidly : 

1.     8  11  9  11  10  8  12 

10  7  10  9  10  11  6 


2.  8 

13 

7 

6 

14 

7 

14 

12 

5 

12 

13 

2 

13 

_5 

3.  14 

15 

16 

5 

16 

3 

16 

6 

.  4 

_3 

15 

2 

15 

J 

4.  2 

18 

3 

2 

19 

0 

1 

17 

1 

17 

18 

0 

17 

19 

i  DRILL  TESTS  35 

DRILL  TEST.     ADDITION 

Add,  and  state  the  answers  rapidly : 

1.  112  2233  12  3 
1  2  22333344 
2313334434 


2.  4 

4 

4 

5 

5 

5 

5 

5 

5 

4 

4 

3 

4 

2 

0 

5 

0 

3 

5 

6 

4 

5 

5 

5 

4 

5 

6 

6 

6 

5 

3.  6 

5 

•  7 

8 

8 

5 

8 

9 

9 

9 

4 

7 

6 

7 

8 

8 

7 

0 

9 

8 

7 

6 

8 

7 

6 

7 

9 

8 

7 

9 

DRILL  TEST.     SUBTRACTION 

Subtract,  and  state  the  answers  rapidly : 

1.  19  18  19  18  19  18  17 

1  2  3  6  7  6  5 


2.  17 

16 

15 

17 

16 

15 

14 

6 

3 

5 

7. 

8 

7 

_8 

3.  14 

13 

12 

14 

13 

12 

14 

9 

_9 

7 

6 

8 

6 

6 

4.  12 

11 

10 

12 

11 

10 

11 

5 

4 

7 

8 

6 

3 

7 

For  "  Busy  Work  "  encourage  the  pupils  to  write  problems  fitting  such 
additions  and  subtractions  as  those  given  on  this  page. 


86 


USING  WHAT  YOU  HAVE  LEARNED 


VII.   USING  WHAT  YOU  HAVE  LEAENED 


PROBLEMS  ABOUT  OUR  CLASS 

1.  If  there  are  14  boys  and  15  girls  in  our  class,  how 
many  pupils  are  there  in  all  ? 

2.  Using  the  numbers  in  Ex.  1,  how  many  more  girls 
than  boys  are  there  in  the  class  ? 

3.  If  14  boys  and  15  girls  belong  in  our  room,  and  1  boy 
and  1  girl  are  absent,  how  many  pupils  are  here  to-day  ? 

4.  If  there  are  29  pupils  in  our  class,  and  5  less  in  the 
class  below  ours,  how  many  are  there  in  that  class  ? 

r  ',  5.  If  there  are  14  boys  in  our  class,  and  9  of  them  form 
a  baseball  team,  how  many  boys  of  our  class  are  not  on 
the  baseball  team? 


APPLICATIONS  37 

PROBLEMS  ABOUT  OUR  STORE 

1.  Fred  went  to  the  store  and  bought  a  pencil  for  5^  and 
a  pad  of  paper  for  6^.   How  much  did  he  pay  for  both? 

2.  Mary  bought  an  eraser  for  5^,  a  ruler  for  10^,  and  a 
penholder  for  3  ^.   How  much  did  she  pay  for  all  ? 

3.  The  teacher  bought  a  box  of  crayons  for  30^  and  a 
blackboard  pointer  for  8^.  How  much  did  she  pay  for  both? 

4.  Jennie's  mother  sent  her  to  the  baker's  for  some  httle 
cakes.  Jennie  bought  6  of  one  kind  and  8  of  another  kind. 
How  many  did  she  buy  in  all  ? 

5.  I  bought  a  bottle  of  ink  for  10^,  some  pens  for  8^, 
and  a  pencil  for  5  ^.   How  much  did  I  pay  for  all  ? 

6.  The  teacher  bought  a  box  of  colored  crayons  for  60^. 
She  gave  the  dealer  75^.  How  much  money  did  he  give 
back  to  her? 

7.  Rob  bought  some  candy  for  5^,  an  apple  for  2^,  and 
an  orange  for  6^.    How  much  did  he  pay  for  all? 

^j^  8.  At  our  store  they  sell  colored  pencils  for  15^  a  box. 
If  I  buy  a  box  and  give  the  dealer  25^,  how  much  money 
does  he  give  back  to  me  ? 

9.  Make  up  a  problem  about  buying  things  at  a  store, 
using  some  of  these  prices : 

Bottle  of  black  ink,  10(^  Pens,  6  for  5  (^ 

Bottle  of  red  ink,  10(^  Pad  of  paper,  6(^  or  8(^ 

Penholder,  4(^  Ruler,  10^ 

Pencil,  3(^,  5(^,  or  8(^  Box  of  toy  money,  25^ 


dfif  FRACTIONS 

VIII.   FRACTIONS 

I-  V        .     *  f 

■,;•  ■  ■  H  irV;  V    .  ;. 

One  Half.   You  may  abeady  know  what  we, mean  by 
one  half  of  anything,  or  by  one  half  of  a  number. 

This  picture  shows  a  sphere,  and  also  shows  a  sphere 
cut  in  two  halves. 

To  find  half  of  a  nurriber  we  divide 
the  number  by  2. 

One  half  is  written  hke  this  :  J. 

We  write  two  halves,  which  equals  1,  like  this :  f . 

If  we  cover  a  half  sphere  in  the  picture,  we  leave  a 
sphere  and  a  half.    One  and  one  half  is  written  1|^. 

ORAL  EXERCISE 

1.  How  much  is  1  of  4?  1  of  8?  ^  of  10? 


2.  Divide  16  by  2  and  so  find  J  of  16. 

3.  How  much  is  1  of  14?  i  of  20?  i  of  18? 

4.  How  much  is  J  of  a  pound  and  J  of  a  pound? 


WRITTEN  EXERCISE 

1.  "Write  in  figures :  two  and  a  half. 

2.  Write  in  figures :  three  and  a  half. 

Copy  and  add : 

3.  J  +  i  31  +  1  11  +  1  214-1 
4.1+1  41  +  1  51  +  1  61  +  1 
5.  Two  halves  are  howmany  ?  Four  halves  are  h6wiUany  ? 


HALVES  AND  FOURTHS 


39 


ORAL  EX:p:RCIS£ 

1.  What  part  of  the  sphere  is  (7? 

2.  JB  is  how  many  times  as  large  as  C? 

3.  If   you   write   one   half   ^,  how   should   you 
one  fourth?   one  third? 

4.  If  you  put  two  fourths 
of  a  sphere  together,  what  part 
will  you  have  ? 

5.  Add  J  of  a  sphere  and  J  of  a  sphere.   Add  J 
sphere,  j-  of  a  sphere,  and  ;|-  of  a  sphere. 


write 


Fourths.    We  write  J  for  one  fourth,  J  for  two  fourths, 
and  j  for  three  fourths.    ^  is  J  of  a  sphere. 
You  have  now  seen  that 

l  +  l  =  f,  and  that  1  =  1; 
J  +  J  =  |,  and  that  f  =  J. 

One  fourth  is  also  called  a  quarter. 


WRITTEN  EXERCISE 

1.  Draw  a  line.    Divide  it  into  halves. 

2.  Draw  another  line  of  the  same  length.  Divide  it  into 
fourths.    How  many  fourths  do  you  find? 

3.  Draw  a  square.    Divide  it  into  fourths.    How  many 
fourths  do  you  find  ? 

4.  Draw  a  line.    Divide  it  into  halves  and  also  into 
fourths.    How  many  fourths  do  you  find  in  one  half? 


40  FRACTIONS 

ORAL  EXERCISE 

1.  Point  to  J  of  these  sqiiares.  How  many  squares  are 
J  of  8  squares? 

2.  Show  that  ^  of  this  oblong  equals 
2  fourths,  and  also  that  4  fourths  of  the 
oblong  is  the  whole. 

3.  How  many  squares  are  J  of  8  squares  ?  Point  to  them 
in  two  different  groups.  How  many  halves  make  the  whole? 

WRITTEN  EXERCISE 

1.  Draw  a  square  2  inches  on  a  side.  Divide  it  into 
squares  each  1  inch  on  a  side.  Each  small  square  is  what 
part  of  the  large  one  ? 

2.  Draw  an  oblong  1  inch  high  and  2  inches  long. 
Divide  it  into  squares  each  1  inch  on  a  side.  Each  square 
is  what  part  of  the  oblong  ? 

3.  If  a  square  is  2  inches  on  a  side,  how  far  is  it  around 
the  square?  Draw  the  square  and  divide  it  into  squares 
each  1  inch  on  a  side. 

4.  Draw  a  square  that  is  1  inch  high,  and  another  that 
is  2  inches  high.  The  first  of  these  squares  is  what  part 
as  large  as  the  second? 

5.  Draw  a  line  and  divide  it  into  fourths.  How  much 
must  you  add  to  ^  of  the  line  to  make  the  whole  hne  ? 

6.  Draw  an  oblong  like  the  one  at  the  top  of  this  page, 
,  and  divide  it  into  8  squares.   Put  stars  in  three  fourths  of 

the  squares. 


PAKTS  OF  A  GEOUP  41 

ORAL  EXERCISE 

1.  How  many  marks  are  ^  of  6  marks?  Ill   III 

2.  How  many  dots  are  J^  of  8  dots  ?  •  •    •  • 

3.  How  many  stars  are  ^  of  10  stars  ?  ***** 

4.  How  many  marks  are  J  of  12  marks  ?  1 1 1 II I   1 1 1!  II 

5.  How  many  dots  are  ^  of  8  dots  ?  •  •  •  • 

Read  and  learn  : 

6.  1  of  2  is  1  1  of  6  is  3  J  of  10  is  5 

7.  1  of  4  is  2  1  of  8  is  4  J  of  12  is  6 

8.  J  of  4  is  1  1  of  8  is  2  J  of  12  is  3 

WRITTEN  EXERCISE 

1.  Make  12  marks  to  show  that  J  of  12  is  3. 

2.  Make  10  stars  to  show  that  1  of  10  is  5. 

3.  If  John  has  12^  and  Rob  has  ^  as  much,  how  much 
has  Rob? 

4.  If  a  boy  10  years  old  has  a  sister  who  is  J  as  old,  how 
old  is  the  sister  ? 

5.  If  a  man  is  6  feet  tall  and  his  son  is  |-  as  tall,  how 
tall  is  his  son? 

6.  There  are  12  inches  in  one  foot.    How  many  inches 
are  there  in  J  of  a  foot  ? 

7.  How  many  inches  are  there  in  J  of  a  foot  ? 
Copy,  and  write  the  answers : 


8.  1  of  8 

lof  10 

iof  2 

J  of  6 

Iof  1' 

9.  1  of  4 

Jof  12 

iof  8 

Iof  4 

4  of  12 

42 


FRACTIONS 


ORAL  EXERCISE 

1.  We  call  12  things  a  dozen,  and  we  write  1  doz.  for 
one  dozen.    How  many  cubes  make  a  dozen  cubes  ? 

2.  There  are  12  inches  in  a  foot.  What  other  name  can 
you  give  to  a  dozen  inches  ? 

3.  Name  some  things  that  are  sold 
by  the  dozen.    Can  you  tell  the  price  ? 

4.  How  many  cubes  make  a  half 
dozen  cubes  ?  How  many  cubes  make 
a  quarter  of  a  dozen  cubes  ?   Point  to  the  cubes  in  giving 
each  answer. 

5.  How  many  fours  do  you  see  in  a  dozen  ?  How  many 
threes  ?  How  many  twos  ?  How  many  sixes  ?  Point  to 
the  cubes  in  giving  each  answer. 

6.  A  hen  sits  on  a  dozen  eggs  and  hatches  all  but  two. 
How  many  chickens  are  hatched  ? 

7.  When  eggs  are  worth  40^  a  dozen,  how  much  does  a 
half  dozen  cost  ?  .     . 

8.  A  newsboy  buys  a  dozen  papers  for  8^,  and  sells  them 
at  a  cent  apiece.   How  much  does  he  make  ? 


9.  John  had  a  dozen  firecrackers.  When  they  were 
lighted,  all  but  J  of  them  exploded.  How  many  fire- 
crackers failed  to  explode  ?   How  many  exploded  ? 


MEASURES 


43 


IX.  MEASURES 


ORAL  EXERCISE 


1.  What  measure  is  Will  using  to  find  the  length  of  the 
blackboard  ?  The  measure  is  how  many  inches  long  ? 

2.  What  measure  is  Mary  using  to  find  the  height  of 
the  blackboard  ? 

3.  How  many  feet  in 
length  is  the  yardstick? 
Measure  it  and  see. 

4.  Measure  the  length 
of  your  own  blackboard 
in  feet ;  in  yards. 

5.  How  many  feet  do 
you  think  the  chalk  rack 
is  from  the  floor  ?  Meas- 
ure the  height  and  see. 

6.  If  your  height  is 
1  yard  and  1  foot,  how 
many  feet  tall  are  you? 

7.  How  many  feet  are  there  in  1  yard  and  2  feet  ? 


Length.    In  measuring  lengths, 

12  inches  =  1  foot 
3  feet  =  1  yard 

We  write  in.  for  inch  or  inches,  ft.  for  foot  or  feet, 
yd.  for  yard  or  yards,  2  ft.  3  in.  for  2  feet  and  3  inches. 


EP 


44  MEASURES 

MEASURING  EXERCISE 

1.  A  yard  is  how  many  times  as  long  as  a  foot? 

2.  Measure  the  width  of  the  room  in  yards,  omitting 
parts  of  a  yard.    Measiire  this  distance  in  feet. 

3.  Look  at  the  foot  rule.    Point  to  1  in.  on  the  rule ; 
point  to  6  in.    How  many  inches  are  there  in  a  foot  ? 

4.  Draw  a  line  one  foot  long  and  divide  it  into  inches. 
How  many  inches  are  6  in.  and  6  in.? 

5.  Point  to  3  in.    How  many  inches  are  there  in  1  ft. 
less  3  in.?    How  many  inches  are  there  in  1  ft.  3  in.? 

6.  Point  to  4  in.    How  many  inches  are  there  in  1  ft. 
less  4  in.?   How  many  inches  are  there  in  1  ft.  4  in.? 

7.  Draw  a  line  that  you  think  is  1  ft.  long.  Measure  it. 

8.  Draw  a  line  that  you  think  is  6  in.  long.  Measure  it. 

9.  Is  the  edge  of  your  desk  more  than  a  foot  long  or 
less  than  a  foot  long?   Measure  it. 

10.  Is  your  desk  more  than  a  foot  high  or  less  than  a 
foot  high?   Measure  it. 

11.  Cut  a  piece  of  string  that  you  think  is  1  yd.  long. 

12.  Draw  a  line  that  you  think  is  1  in.  long.  Measure  it. 

13.  How  many  inches  are  there  in  1  ft.  less  5  in.  ? 

14.  How  many  inches  are  there  in  1  ft.  less  8  in.? 

15.  Draw  a  line  that  you  think  is  24  in.  long.  Measure  it. 

The  children  should  be  given  much  practice  in  using  real  measures. 
They  should  also  exercise  their  judgment  in  estimating  lengths.  A  yard- 
stick and  a  ruler  divided  into  inches,  half  inches,  and  quarter  inches  are 
desirable  for  this  grade. 


LIQUID  MEASURE 


45 


ORAL  EXERCISE 

1.  Which  is  the  pint  measure  in  the  picture,  and  which 
is  the  quart  ? 

2.  How  many  pints 
make  a  quart?  A  pint 
is  what  part  of  a  quart? 

3.  Tell  me  the  names 
of  several  things  that 
are  sold  by  the  pint  and 
the  names  of  others  that 
are  sold  by  the  quart. 

4.  Draw  a  full-sized 
picture  of  a  quart  meas- 
ure. Draw  a  line  across 
it,  marking  off  1  pint. 

5.  How  much  is  10  quarts  + 1  quart  + 1  quart  + 1  quart? 


Liquid  Measure.    In  measuring  liquids, 

2  pints  =  1  quart 

We  write  pt.  for  pint  or  pints,  and  qt.  for  quart  or 
quarts.   A  pint  is  J^  of  a  quart. 


6.  How  much  does  a  quart  of  milk  cost  where  we  live  ? 
How  much  does  a  pint  of  milk  cost  ? 

7.  If  I  have  a  quart  of  cream  and  a  pint  of  cream,  how 
many  pints  of  cream  do  I  have  ? 


46 


MEASURES 


ORAL  EXERCISE 

1.  The  children  in  the  picture  have  a  2-pound  weight 
and  a  i-pound  weight  to  balance  the  book.  Tell  me  how 
much  the  book  weighs. 

2.  Suppose  the  chil- 
dren should  weigh  1  pt. 
of  water  and  find  that 
it  weighs  a  pound,  how 
much  would  1  qt.  weigh? 

3.  If  one  of  your 
books  weighs  ^  pound, 
another  J  pound,  and 
a  third  J  pound,  how  much  do  all  three  books  weigh? 

4.  If  the  children  had  a  pound  of  figs  worth  2  dimes, 
how  much  would  ^  pound  of  these  figs  be  worth? 


Pounds.  We  write  lb.  for  pound  or  pounds.    Thus,  2  lb. 
means  2  pounds,  and  J  lb.  means  J  of  a  pound. 


5.  Add  20  lb.,  10  lb.,  and  1  lb. 

6.  Add  9  lb.,  4  lb.,  2  lb.,  and  1  lb. 

7.  Find  1  of  4  lb.,  J  of  6  lb.,  and  1  of  2  lb. 

8.  From  69  lb.  subtract  4  lb.  and  then  add  1  lb. 

9.  From  87  lb.  subtract  10  lb.,  6  lb.,  and  1  lb. 

It  is  desirable  that  children  should  weigh  various  objects,  using  the 
pound,  half  pound,  and  quarter  poxind.  The  table  of  pounds  and  ounces  is 
taken  up  later. 


KEVIEW  DRILL  47 

X.   REVIEW  DRILL 
ORAL  EXERCISE 

Add  each  of  the  numbers  2,  3,  4,  5,  6,  7,  8,  9,  to : 


1.  31 

51 

81 

21 

71 

41 

61 

91 

11 

2.  42 

82 

22 

72 

52 

12 

2 

32 

62 

3.  83 

33 

73 

3 

13 

63 

43 

23 

53 

4.  64 

44 

74 

4 

34 

84 

14 

54 

24 

5.  45 

85 

75 

15 

55 

25 

5 

65 

35 

6.  56 

46 

6 

36 

66 

26 

76 

16 

86 

7.  47 

67 

27 

87 

77 

37 

57 

7 

17 

8.  58 

48 

78 

18 

88 

68 

28 

8 

38 

9.  79 

39 

89 

69 

29 

9 

19 

49 

59 

Subtract  each 

of  the  numbers  2, 

3,  4,  5,  6,  7,  8, 9,  from: 

10.  40 

70 

90 

10 

50 

80 

20 

60 

30 

11.  51 

71 

41 

61 

31 

91 

11 

81 

21 

12.  72 

52 

12 

42 

82 

62 

22 

92 

32 

13.  33 

23 

93 

83 

63 

13 

73 

53 

43 

14.  64 

14 

44 

74 

54 

24 

84 

34 

94 

15.  95 

85 

65 

15 

45 

25 

85 

55 

75 

16.  96 

46 

86 

56 

36 

66 

16 

76 

26 

17.  47 

97 

57 

37 

87 

17 

67 

27 

77 

In  exercises  of  this  nature  it  is  not  expected  that  teachers  will  require 
all  of  the  work.  As  soon  as  the  pupils  show  themselves  proficient  in  the 
additions  and  subtractions  they  should  pass  to  the  next  topic. 


48  EEVIEW  DRILL 


DRILL  TEST.     FRACTIONS  AND  MEASURES 

State  the  answers  rapidly : 

1.  1  of  4         1  of  2         1  of  10         1  of  6 

iof8 

2.  1  of  4         i  of  8         i  of  12         1  of  4 

}of  4 

3.  1  of  12  in.         1  of  1  doz.         i  of  8  ft. 

Jof  $6 

4.  1  of  12  in.         1  of  1  doz.         J  of  8  yd. 

iof60 

5.  In  1  yd.  there  are  (?)  ft.   A  foot  is  (?)  of  a  yard. 

6.  In  1  ft.  there  are  (?)  in.;  in  2  ft.  there  are  (?)  in. 

7.  In  1  qt.  there  are  (?)  pt.   A  pint  is  (?)  of  a  quart. 

8.  1  of  a  pound  and  J  of  a  pound  are  (?)  pound. 

9.  1+i  11  +  1  11  +  1  21  +  1 

10.  1  +  1  11  +  1  2  +  1  21  +  1 

11.  1^  of  a  sphere  and  \  of  the  same  sphere  make  (?). 

12.  ^  of  a  pound  and  J  of  a  pound  and  J  of  a  pound 
make  (?)  poimd. 

13.  In  1  qt.  there  are  (?)  pt.;  in  2  qt.  there  are  (?)  pt. 

14.  In  1  yd.  there  are  (?)  ft. ;   in  2  yd.  there  are  (?)  ft. 

15.  In  1  ft.  there  are  (?)  in.;  in  2  ft.  there  are  (?)  in. 

16.  A  foot  is  (?)  in.  more  than  i  ft. 

17.  A  yard  is  (?)  ft.  more  than  1  ft. 

18.  A  quart  is  (?)  pt.  more  than  1  pt. 

19.  A  nickel  is  (?)  cents,  and  2  nickels  make  (?)  dime, 
or  (?)  cents. 

20.  In  $1  there  are  (?)  dimes,  or  (?)  cents. 

21.  In  3  yd.  there  are  (?)  ft.;  in  4  yd.  there  are  (?)  ft. 


USING  WHAT  YOU  HAVE  LEARNED 


49 


XL   USING  WHAT  YOU  HAVE  LEARNED 


ORAL  EXERCISE 

1.  Fred's  father  gives  him  3^  an  hour  for  weeding  the 
garden.    How  mnch  does  Fred  earn  in  2  hours? 

2.  If  Fred  works  long  enough  to  earn  30^,  and  then  buys 
a  25-cent  ball,  how  much  does  he  have  left  ? 

3.  K  he  wishes  to  buy  an  orange  that  costs  3  ^,  how  long 
will  he  have  to  work  to  earn  the  money  ? 

4.  How  much  does  a  good  rubber  ball  cost?  If  Fred 
has  24^,  is  this  too  much  or  too  httle  to  buy  the  ball? 

5.  Fred  has  1^  in  his  pocket.  If  he  earns  3^  an  hour, 
how  long  will  it  take  him  to  earn  9  ^,  so  that  he  can  buy 
10^  worth  of  marbles? 


50 


USING  WHAT  YOU  HAVE  LEARNED 


6.  Julia's  aunt  wishes  to  show  her  what  it  means  to 
earn  money.  She  pays  her  4^  an  hour.  Juha  worked  half 
an  hour  this  morning  before  school.  How  much  did  she 
earn  then? 

7.  After  school  Julia  worked  an  hour.  How  much  has 
she  earned  to-day? 

8.  Julia  wished  to  earn  enough  to  buy  15^  worth  of 
ribbon.  After  she  worked  2  hom-s  at  4^  an  hour  had  she 
enough  ?  Had  she  enough  after  she  worked  3  hours  ?  How 
much  did  she  then  lack  ? 

9.  After  Julia  had  worked  4  hours  she  found  she  had 
earned  more  than  enough  for  her  ribbon.  How  much  more  ? 

There  is  always  some  advantage  in  letting  a  pupil  do  simple  multi- 
plication by  means  of  addition.  It  makes  the  subject  of  multiplication 
seem  more  valuable  when  it  is  reached. 


EEVIEW  51 

10.  Fred's  father  sent  him  to  the  store  to  buy  a  basket. 
He  gave  Fred  a  25-ceiit  piece.  Fred  paid  20^  for  the  basket. 
How  much  money  did  he  have  left  ? 

11.  Fred  saw  at  the  store  a  baseball  mitt.  He  has  saved 
40^  toward  buying  it.  The  mitt  costs  50^.  How  much 
more  money  must  he  have? 

12.  Juha's  aunt  sent  her  to  the  store  to  buy  a  dozen  eggs. 
Juha  finds  that  they  have  only  J  doz.  to  sell.  How  many 
eggs  must  she  buy  at  another  store  to  make  up  the  dozen  ? 

13.  Julia  pays  20^  for  i  doz.  eggs.  How  much  would 
she  have  to  pay  for  a  dozen  ? 

14.  Julia's  aunt  sends  her  to  buy  2  qt.  of  milk.  If  Julia 
pays  8^  for  a  quart,  how  much  does  she  pay  for  2  qt.? 

15.  Fred  is  sent  to  the  store  to  buy  ^  doz.  bananas. 
How  many  bananas  does  he  buy  ? 

16.  If  Fred  buys  1 J  doz.  oranges,  how  many  oranges 
does  he  buy?  First  find  how  many  oranges  there  are  in 
a  dozen,  then  in  ^  doz.,  and  then  in  1^  doz. 

17.  Fred  pays  8^  for  some  salt,  and  gives  the  storekeeper 
a  dime.   How  much  change  does  he  get  back  ? 

18.  Julia  is  making  some  doll's  clothes.  She  needs  J  yd. 
of  ribbon  which  costs  12^  a  yard.  How  much  must  she 
pay  fori  yd.? 

19.  Julia's  aunt  asks  her  to  find  how  much  the  breakfast 
cost.  Julia  found  that  the  oatmeal  cost  10^,  the  milk  5^, 
the  bread  and  butter  4^,  and  the  meat  20^.  How  much 
did  she  find  that  all  these  cost  ? 


62  LITTLE  EXAMINATIONS 

XII.  LITTLE  EXAMINATIONS 


II. 


III. 


IV. 


V. 


1. 

3  +  9. 

5. 

iof8. 

9. 

2  pt.  =  (?)  qt. 

2. 

17-8. 

6. 

i  of  12. 

10. 

lyd.  =  (?)ft. 

3. 

22  +  6. 

7. 

Jof  8(^. 

11. 

H  +  h 

4. 

45  -  30. 

8. 

1  of  6^. 

12. 

12  +  23  +  2. 

1. 

5  +  8. 

5. 

1  of  8  ft. 

9. 

4pt.  =  (?)qt. 

2. 

14-6. 

6. 

i  of  8  ft. 

10. 

1  ft.  =  (?)  in. 

3. 

42+10. 

7. 

i  of  12. 

11. 

21+3. 

4. 

62-31. 

8. 

1  of  12. 

12. 

23  +  45  +  1. 

1. 

37  +  6. 

5. 

1  of  10  f 

9. 

lpt.  =  (?)qt. 

2. 

14-7. 

6. 

1  of  8  in. 

10. 

2yd.  =  (?)ft. 

3. 

52  +  13. 

7. 

i  of  12  lb. 

11. 

^  +  i^ 

4. 

74-21. 

8. 

1  of  12  qt. 

12. 

51  +  6  +  11. 

1. 

54  +  8. 

5. 

1  of  10. 

9. 

6pt.  =  (?)qt. 

2. 

13-5. 

6. 

i  of  $10. 

10. 

2  ft.  =  (?)in. 

3. 

38  +  20. 

7. 

1  of  12  f 

11. 

3  +  21 

4. 

66  -  22. 

8. 

i  of  112. 

12. 

31  +  22  +  12 

1. 

77  +  7. 

5. 

1  of  20. 

9. 

2qt.  =  (?)pt. 

2. 

13-6. 

6. 

J  of  14. 

10. 

6ft.  =  (?)yd. 

3. 

73  +  14. 

7. 

1  of  12  lb. 

11. 

H^h 

4. 

79-32." 

8. 

i  of  16. 

12. 

33  +  40  +  1. 

These  Little  Examinations  at  the  close  of  each  chapter  furnish  excellent 
review  drill  work.  The  time  should  be  recorded  for  each,  and  the  pupils 
should  endeavor  to  improve  their  records.  This  work  may  be  used  for  review 
in  the  first  part  of  the  next  chapter. 


CHAPTER  II 


I.   NUMBERS  TO  1000 


ORAL  EXERCISE 

1.  Here  are  4  bundles  of  splints,  10  in  a  bundle.    How- 
many  splints  are  there  ?   Write 
the  number  on  the  blackboard.      ^^      '^^     S^ 

2.  If  there  are  5  such  bundles 
of  splints,  how  many  splints 
are  there  in  all?   Write  the  number  on  the  blackboard. 

3.  Here  are  3  bundles  of  spHnts,  100  in  a  bundle.  How 
many  splints  are  there?  Write  the 
number  on  the  blackboard.  If  there 
were  400  more,  how  many  splints 
would  there  be?  Write  the  number 
on  the  blackboard. 

4.  Here  is  a  larger  bundle  of  splints, 

containing  as  many  splints  as  there  are  in  10  bundles  of 
100  each.    How  many  sphnts  are  there  in 
this  bundle  ? 

5.  How  many  lO's  are  there  in  100? 
How  many  lOO's  are  there  in  1000?  What 
is  the  name  for  ten  10' s?  What  is  the 
name  for  ten  lOO's  ? 

53 


54 


NUMBEKS  TO  1000 
ORAL  EXERCISE 

1.  How  many  splints  are  there  in  the  picture? 


300 


+ 


40      +     2 


203 

110 

123 

105 

890 

987 

705 

111 

999 

2.  Read  these  numbers : 

342  372  100  101 
352  392  200  202 
362       312       302       102 

3.  Open  this  book  at  page  146  ;  at  page  110. 

4.  The  numbers  below  10  are  called  ones.  For  example, 
6  is  six  ones.  We  write  the  ones  in  the  right-hand  place. 
In  the  number  26  there  are  2  tens  and  6  ones.  Where  do 
we  write  the  tens  f   Where  do  we  write  the  hundreds  ? 

5.  Name  the  figure  in  ones'  place  in  475;  the  figure 
in  tens'  place;  the  figure  in  hundreds'  place. 


WRITTEN  EXERCISE 

1.  Write  in  figures : 

Five  hundred  fifty-five 
Two  hundred  forty-nine 
One  hundred  twenty-one 

2.  Write  in  words  : 
242       207       520       634 


Six  hundred  nine 
Three  hundred  three 
Eight  hundred  eighty 


987       843       765 


BEADING  AKD  WRITING  NUMBERS 


55- 


ORAL  EXERCISE 

Head  these  numbers : 

1.  208        210        217        237        286  506        242 

2.  348        376        407        473        530  721        346 

3.  691        682        707        827        936  888        989 

4.  What  is  the  ones'  figure  in  450?  the  tens'  figure? 
the  hundreds'  figure  ? 

WRITTEN  EXERCISE 


Write  in  figures : 

1.  One  hundred  one 

2.  Two  hundred  three 

3.  Three  hundred  six 

4.  Four  hundred  lyne 

5.  Six  hundred  six 


One  hundred  fifty 
Two  hundred  seventy 
Three  hundred  ninety 
Five  hundred  forty 
Seven  hundred  eight 


Write  in  words : 

6.  527    642    334 

7.  708    860    901 

Write  in  figures : 

8.  Forty-three 

9.  Twenty-one 

10.  Fifty-two 

11.  Seventy-eight 

12.  Five  hundred 

13.  Six  hundred 

14.  Seven  hundred 


456 

777 


678 
800 


909 
750 


742 
630 


830 
400 


303 
1000 


Eight  hundred  seventy-seven 
Seven  hundred  eighty-nine 
Nine  hundred  ninety-nine 
Six  hundred  seventy-eight 
Five  hundred  sixty-seven 
Six  hundred  seventy-three 
Seven  hundred  twenty-seven 


56 


NUMBERS  TO  1000 


ORAL  EXERCISE 

1.  Read  the  figures  on  the  clock. 

2.  Which  hand  tells  the  hours?  Which  tells  the  minutes? 

3.  How  long  does  it  take  the 
hour  hand  to  pass  from  I  to  II? 
How  long  does  it  take  the  minute 
hand  to  pass  from  I  to  II  ? 

4.  How  long  does  it  take  the 
hour  hand  to  pass  around  from 
XII  to  XII  again?  How  long 
does  it  take  the  minute  hand? 

5.  What  time  is  it  by  the  clock 
in  the  picture?   What  time  is  it  by  the  school  clock? 

6.  How  many  minutes  in  an  hour  ?  in  ^  hour  ? 


Roman  Numerals.  The  figures  often  seen  on  clocks  are 
called  Roman  numerals,  and  are  as  follows : 

I   II   III   mi  or  IV   V   VI   VII   VIII   IX  X   XI   XII 
123  4  567        8       9    10   11     12 

Time.    Read  and  learn : 

60  minutes  =  1  hour 
24  hours  =  1  day 

We  write  min.  for  minute  or  minutes,  hr.  for  hour  or 
hours,  da.  for  day  or  days,  a.m.  for  forenoon,  and  p.m.  for 
afternoon.  We  write  15  minutes  after  2  in  any  of  these 
three  ways :  2  15,  2  :  15,  or  2  hr.  15  min. 


>- 

ADDITION 

67 

II.  ADDITION 

ORAL  REVIEW  DRILL 

Add 

^Ae  following : 

1.  6 

16 

26 

96  ' 

7 

27 

47 

87 

3 

3 

3 

3 

5 

5 

5 

5 

2.  4 

14 

34 

64 

5 

37 

55 

25 

7 

7 

7 

7 

6 

6 

6 

6 

3.  8 

28 

48 

78 

3 

13 

33 

53 

4 

4 

4 

4 

8 

_^ 

8 

8 

4.  9 

39 

59 

89 

7 

37 

57 

87 

2  ■ 

2 

2 

2 

9 

9 

9 

9 

5.  3 

43 

43 

65 

2 

35 

48 

62 

9 

9 

8 

7 

8 

6 

7 

8 

6.  7 

37 

58 

58 

8 

68 

52 

63 

8 

8 

8 

7 

6 

6 

9 

9 

7.  6 

26 

46 

46 

6 

56 

27 

38 

6 

6 

6 

8 

7 

7 

7 

7 

8.  9 

49 

79 

79 

8 

38 

57 

69 

9 

9 

9 

7 

8 

8 

8 

8 

9.  7 

57 

58 

79 

4 

34 

37 

38 

4 

4 

4 

5 

9 

9 

5 

6 

10.  4 

63 

54 

84 

5 

95 

94 

97 

8 

8 

8 

4 

5 

5 

6 

3 

58  ADDITION 

ORAL  EXERCISE 

1.  If  you  have  12  marbles  and  6  marbles,  how  many  do 
you  have  in  all? 

2.  If  you  have  12  (^  and  10  ^,  how  much  do  you  have  in  all  ? 

3.  If  there  are  11  girls  and  10  boys  in  the  class,  how 
many  children  are  there  in  all? 

Add  the  following : 

4.  12  12  12  20  25  35  48 

6  8  10  20  20  20  30 


5.  50 

51 

57 

58 

67 

22 

35 

30 

30 

30 

40 

30 

11 

11 

1 
Add  the  following 

WRITTEN  EXERCISE 

1.  30 

32 

32 

42 

45 

87 

40 

40 

45 

35 

32 

3 

2.  33 

33 

63 

63 

64 

76 

60 

66 

30 

36 

35 

4 

3.  70 

74 

74 

75 

74 

93 

24 

20 

21 

23 

25 

7 

4.  160 

166 

166 

176 

277' 

342 

200 

210 

213 

223 

322 

523 

5.  273 

428 

579 

343 

628 

496 

401 

320 

210 

343 

231 

300 

TWO-FIGURE  NUMBERS 


59 


46 

37 
13  = 

sum 

of  ones 

7    = 

sum 

of  tens 

83  = 

sum 

of  numbers 

Adding  Two-Figure  Numbers.   1.  If  I  have  46^  and  37^, 
how  much  money  have  I  in  all  ? 
I  may  think  of  46  and  37  like  this : 

46  =  40  +    6,  or  4  tens  and    6  ones 
37  =  30  +    7,  or  3  tens  and    7  ones 
The  sum  is      70  +  13,  or  7  tens  and  13  ones,  or  83 

The  teacher  should  put  the  above 
solution  on  the  blackboard,  and  should 
lead  the  pupils  to  see  that  they  might 
add  the  ones  and  tens  separately,  as 
here  shown.  This  is  too  long,  however, 
and  so  we  add  without  all  this  work. 

We  add  the  numbers  as 
shown  below. 

We  see  that  7  ones  and  6  ones  are  13  ones, 
and  we  write  the  3  in  the  ones'  column  and  add 
the  1  to  the  tens. 

Then  1  +  3  +  4  =  8,  and  we  write  the  8  in  the 
tens'  column. 

The  sum  is  83,  and  so  I  have  83^  in  all. 

2.  If  I  have  24  marbles,  38  marbles,  and  16  marbles, 
how  many  marbles  have  I  in  all? 

We  add  the  numbers  as  here  shown. 

We  see  that  the  sum  of  the  ones  is  6  +  8  +  4, 
or  18,  and  we  write  the  8  in  the  ones'  column 
and  add  the  1  to  the  tens. 

Then  1  +  1  +  3  +  2  =  7,  and  we  write  the  7 
in  the  tens'   column. 

The  sum  is  78,  and  so  I  have   78  marbles  in  all. 


46 
37 

83 


24 
38 
16 

78 


60  ADDITION 

WRITTEN  EXERCISE 


Add 

the  following 

'•' 

1.  24 

23 

23 

21 

25 

35 

65 

36 

37 

38 

39 

39 

17 

25 

2.  22 

34 

33 

67 

34 

47 

37 

38 

47 

59 

23 

46 

15 

17 

3.  32 

24 

36 

26 

58 

29 

53 

48 

28 

36 

37 

25 

16 

38 

4.  35 

47 

65 

27 

72 

33 

66 

35 

26 

18 

19 

19 

18 

29 

5.  48 

56 

39 

47 

55 

78 

74 

27 

39 

29 

38 

19 

16 

18 

6.  59 

73 

66 

48 

68 

37 

49 

26 

19 

24 

23 

15 

27 

16 

7.  29 

52 

29 

35 

19 

27 

58 

48 

29 

39 

45 

39 

46 

18 

8.  27 

38 

59 

46 

25 

44 

25 

37 

43 

17 

36 

35 

37 

38 

9.  21 

36 

45 

37 

56 

49 

47 

19 

18 

15 

17 

18 

29 

36 

10.  11 

21 

32 

13 

14 

15 

16 

28 

36 

49 

48 

48 

48 

23 

33 

48 

26 

38 

38 

38 

46 

THEEE-FIGURE  NUMBEES  61 

Adding  Three-Figure  Numbers.    We  often  have  to  add 
numbers  of  three  figures. 

John  worked  on  Saturday  for  Mr.  Eastman,  the  grocer. 
Mr.  Eastman  told  John  to  look  over  two  boxes  of  apples 
and  throw  away  the  bad  ones.  John  found  156  good  apples 
in  one  box  and  117  in  the  other.  How  many 
good  apples  did  he  find  in  all? 

We  see  that  we  must  add  156  and  117. 

7  ones  +  6  ones  =  13  ones  =  1  ten  +  3  ones. 
We  write  the  3  in  the  ones'  column  and  add 
the  1  to  the  tens. 

1  ten  + 1  ten  +  5  tens  =  7  tens.    We  write  the  7  in  the 
tens'  column. 

1  hundred  +  1  hundred  =  2  hundreds.    We  write  the  2 
in  the  hundreds'  column. 

The  sum  is  273,  and  so  John  found  273  good  apples. 

WRITTEN  EXERCISE 

1.  There  are  186  oranges  in  one  box  and  107  in  an- 
other box.    How  many  oranges  are  there  in  both  boxes? 

2.  There  are  127  boys  and  134  girls  in  a  school.   How 
many  pupils  are  there  in  the  school  ? 

3.  Sam  tied  338  ft.  of  string  and  125  ft.  of  string  to 
gether  to  make  a  kite  string.  How  long  was  the  kite  string  ? 

Add  the  following ,  and  check  the  work: 

4.  5.                 6.                7.  8.  9. 
278           346           227           625  506  $329 
104           229           347           135  206  225 


62  ADDITION 

Addition  Continued.  Mr.  Eastman  told  John  to  count 
the  oranges  which  were  left  after  the  day's  sale.  In  one 
box  there  were  172  oranges  and  in  another 
box  156  oranges.  How  many  oranges  were  left 
in  the  two  boxes? 

We  see  that  we  must  add  172  and  156. 

6  ones  +  2  ones  =  8  ones.    We  write  the  8  in 
the  ones'  column. 

5  tens  +  7  tens  =  12  tens  =  1  hundred  -f-  2  tens.  We 
write  the  2  in  the  tens'  column  and  add  the  1  to  the 
hundreds. 

1  hundred  +  1  hundred  +  1  hundred  =  3  hundreds.  We 
write  the  3  in  the  hundreds'  column. 

The  sum  is  328,  and  so  there  are   328   oranges   left. 

The  teacher  will  observe  that  on  page  61  the  sum  of  the  ones  (units) 
was  more  than  10,  while  on  this  page  the  sum  of  the  tens  is  more  than 
10  (tens).   On  page  63  the  general  case  is  considered. 

WRITTEN  EXERCISE 

1.  There  are  140  sheep  in  one  pasture  and  174  sheep  in 
another  pasture.   How  many  sheep  are  there  in  all  ? 

2.  It  is  143  miles  from  here  to  the  place  where  Rob 
lives,  and  162  miles  further  to  the  place  where  James  lives. 
How  far  is  it  from  here  to  the  place  where  James  lives  ? 

Add  the  following ,  and  check  the  ivork: 

3.  4.  5.  6. 
263           374            382            491 
142            251            166            275 


7. 

8. 

282 

$473 

370 

264 

THEEE-FIGURE  NUMBERS  63 

Addition  Continued.  Mr.  Forbes  has  a  comer  lot.  He  is 
building  a  picket  fence  on  the  sides  facing  the  two  streets. 
He  needs  196  pickets  on  one  side  and  188  on  the  other 
side.   How  many  pickets  does  he  need  in  all? 

We  see  that  we  must  add  196  and  188. 

8  ones  +  6  ones  =  14  ones  =  1  ten  +  4  ones. 
We  write  the  4  in  the  ones'  column  and  add 
the  1  to  the  tens. 

1  ten  +  8  tens  +  9  tens  =  18  tens,  or  1  hundred 
+  8  tens.    We  write  the  8  in  the  tens'  column  and  add 
the  1  to  the  hundreds. 

1  hundred  + 1  hundred  + 1  hundred  =  3  hundreds.  We 
write  the  3  in  the  hundreds'  column. 

The  sum  is  384,  and  so  Mr.  Forbes  needs  384  pickets. 

WRITTEN  EXERCISE 

1.  If  Mr.  Forbes  needs  187  pickets  for  a  fence  on  one 
side  of  his  lot  and  165  pickets  for  a  fence  on  another  side, 
how  many  pickets  does  he  need  for  both  sides  ? 

Add  the  following ,  and  cfieck  the  work: 

a.                  3.                  4.                  5,  6.  7. 

288            357            349            281  555  239 

368            285            _68            399  278  471 

8.  9.  10.  11.  12.  13. 

200  301  110  240  125  379 

325  288  229  386  474  206 

295  322  291  285  199  98 


64  SUBTRACTION 

III.  SUBTRACTION 

Subtraction  Reviewed.  If  Louis  has  7  marbles  and  loses 
4  of  them,  he  has  3  marbles  left ;  if  he  has  17  marbles  and 
loses  4  of  them,  he  has  13  marbles  left ;  and  if  he  has  27 
marbles  and  loses  4  of  them,  he  has  23  marbles  left.  That  is, 

7-4=   3  27-4  =  23  47-4  =  43 

17-4=13  37-4  =  33  57-4  =  53 

This  kind  of  drill  on  subtraction  by  endings  is  valuable.  For  example, 
because  8  —  6  =  2,  we  know  that  18  —  6  =  12,  28  —  6  =  22,  and  so  on. 


ORAL  REVIEW  DRILL 

Subtract  the  folloiving  : 

1.  11         21         31         61         10 

20 

30 

70 

2           2           2           2           3 

3 

3 

3 

2.  12 

22 

32 

82 

13 

23 

33 

93 

4 

4 

4 

4 

5 

5 

5 

5 

3.  14 

24 

34 

74 

15 

25 

65 

85 

7 

7 

7 

7 

6 

6 

6 

6 

4.  16 

26 

46 

76 

17 

27 

57 

77 

8 

8 

8 

8 

9 

9 

9 

9 

5.  18 

28 

48 

98 

16 

36 

56 

86 

9 

9 

9 

9 

_7 

7 

7 

7 

6.  15 

25 

14 

34 

12 

32 

11 

41 

7 

7 

8 

8 

6 

6 

7 

7 

•Minuend,  47 
Subtrahend,  28 
Difference,     19 


TWO-FIGURE  NUMBERS  65 

Subtraction  Continued.  When  one  number  is  subtracted 
from  another,  the  larger  number  is  called  the  minuend,  the 
smaller  number  is  called  the  subtrahend,  and  the  result  is 
called  the  difference  or  remainder. 

If  there  are  47  pupils  in  one  room  and  28  pupils  in 
another,   how  many  more  are  there  in  the  first  room? 

We  subtract  as  here  shown. 

We  cannot  take  8  ones  from  7 
ones,  so  we  take  1  ten  of  the  4 
tens  and  put  it  with  the  7  ones, 
making  .17  ones. 

Then  17  ones  —  8  ones  =  9  ones. 

Then  2  tens  from  the  3  tens  remaining  leaves  1  ten. 

The  difference  is  1  ten  and  9  ones,  or  19. 

This  shows  what  we  did,  and  also  shows  the  check. 
47  =  30+17  28 

28  =  20+   8  19 

19  =  10+   9  47 

There  are  two  leading  methods  of  subtraction  used  in  the  business  world. 

1.  We  may  think  of  the  above  numbers  as  follows : 

47  =  40  +  7     or     30  +  17 
28=  20+8 

Subtracting,  we  have  10  +    9  =  19 

This  subtraction  may  be  performed  either  directly,  by  taking  8  from  17, 
and  20  from  30  ;  or  indirectly,  by  thinking  "8  and  9  are  17,  2  and  1  are  3." 

2.  We  may  think  of  both  numbers  as  increased  by  10. 

Instead  of  47  we  shall  have  40  +  17 

Instead  of  28  we  shall  have  30+8 

Subtracting  as  before,  we  have  10  +    9  =  19 

Either  of  these  plans  is  allowable,  and  all  are  used  in  business. 


66 


SUBTEACTION 

WRITTEN  EXERCISE 

Subtract,  and  check : 

1.  53    61    72    81    65 

91 

28    32    28    53    37 

56 

83 

25 


2.  94 

96 

54 

62 

82 

80 

76 

66 

78 

27 

43 

54 

37 

29 

3.  74 

63 

73 

83 

55 

63 

95 

46 

47 

39 

65 

39 

29 

38 

4.  56 

76 

64 

57 

75 

90 

65 

48 

49 

26 

28 

48 

47 

29 

5.  Frank  has  28  marbles  and  Tom  has  43.    How  many- 
more  marbles  has  Tom  than  Frank  ? 

6.  A  schoolroom  is  42  ft.  long  and  28  ft.  wide.    It  is 
how  much  longer  than  wide? 

7.  In  playing  a  game  John's  score  was  31  and  Fred's 
was  19.    Find  the  difference  in  their  scores. 

8.  A  boy  is  12  years  old  and  his  father  is  41  years  old. 
How  much  older  is  the  father  than  his  son  ? 

9.  A  girl  has  a  piece  of  cloth  41  in.  long.    She  cuts  off 
27  in.  for  a  doll's  dress.   How  much  has  she  left? 

10.  There  are  31  children  in  one  class  and  28  in  another. 
Bow  many  more  are  there  in  one  class  than  in  the  other  ? 

11.  A  man  has  92  hens  and  sells  75  of  them.   How 
many  hens  has  he  left? 


THREE-FIGURE  NUMBERS  67 

Subtracting  Three-Figure  Numbers.  If  there  are  701 
children  in  one  city  school  and  240  in  another,  how  many 
more  are  there  in  one  school  than  in  the  other? 

We  see  that  we  must  subtract  240  from  701. 

We  write  the  numbers  as  here  shown. 

We  see  that  1—0  =  1,  and  we  write  the  1 
below  the  0  and  the  1. 

We  cannot  take  4  tens  from  0  tens,  so  we 
take  1  hundred  of  the  7  hundreds,  making  100,  or  10  tens. 

Then  10  tens  —  4  tens  =  6  tens,  and  we  write  the  6  below 
the  4  and  the  0. 

The  7  hundreds  is  now  6  hundreds,  because  we  took 
1  hundred  away. 

Then  6  hundreds  —  2  hundreds  =  4  hundreds,  and  we 
write  the  4  below  the  2  and  the  7. 

The  difference  is  461,  and  so  there  are  461  more  children 
in  one  school  than  in  the  other. 

We  check  the  work  by  adding  240  to  461. 

WRITTEN  EXERCISE 

Subtract,  and  check  the  work : 


1.  732 

743 

754 

765 

708 

802 

250 

270 

290 

283 

296 

591 

2.  583 

842 

927 

916 

823 

730 

291 

391 

645 

424 

460 

263 

3.  839 

819 

829 

935 

708 

820 

567 

577 

577 

442 

523 

575 

68  SUBTRACTION 

Further  Work  in  Subtraction.  If  there  are  731  pupils  in 
one  city  school  and  246  in  another,  how  many  more  are 
there  in  the  first  school  than  in  the  second? 

We  see  that  we  must  subtract  246  from  731. 

To  subtract  246  from  731  we  write  the  num- 
bers as  here  shown. 

We  cannot  take  6  from  1,  so  we  take  1  ten 
of  the  3  tens  and  put  it  with  the  1,  making  11. 

Then  11—6  =  5,  and  we  write  the  5  below  the  6  and  1. 

The  3  tens  are  now  2  tens,  because  we  took  1  ten  away. 
We  cannot  take  4  tens  from  2  tens,  so  we  take  1  hundred 
of  the  7  hundreds  and  put  it  with  the  2  tens,  making  120, 
or  12  tens. 

Then  12  tens  —  4  tens  =  8  tens,  and  we  write  the  8  below 
the  4  and  the  3. 

Then  6  hundreds  —  2  hundreds  =  4  hundreds,  and  we 
write  the  4  below  the  2  and  the  7. 

The  difference  is  485,  and  so  there  are  485  more  pupils 
in  the  first  school  than  in  the  second. 

Another  Example.  If  there  are  700  pupils  in  one  school 
and  246  in  another,  how  many  more  are  there  in  the  first 
school  than  in  the  second  ? 

We  see  that  we  must  subtract  246  from  700. 

We  cannot  take  6  from  0,  or  4  from  0,  so  we 
think  of  700  as  600  +  90  +  10. 

Then  10  —  6  =  4,  9  tens  —  4  tens  =  5  tens,  and 
6  hundreds  —  2  hundreds  =  4  hundreds. 

The  difference  is  454,  and  so  there  are  454  more  pupils 
in  the  first  school  than  in  the  second. 


THREE-FIGURE  NUMBERS  69 

WRITTEN  EXERCISE 

Subtract,  and  check  the  work : 

1.  911  621  722  645  523  821 

385  384  388  387  287  642 


2. 

713 

396 

925 
456 

632 

469 

617 

438 

927 
679 

731 

496 

3. 

515 

296 

651 

392 

834 

688 

722 
485 

722 
433 

832 

468 

4. 

735 

268 

913 

688 

536 

398 

643 

288 

635 

388 

936 

428 

5. 

912 
335 

834 
495 

826 
237 

925 

358 

813 

426 

914 

769 

6. 

716 
328 

814 
227 

841 
356 

922 
488 

833 
539 

644 
298 

7. 

113 
4 

103 

4 

203 
4 

413 
104 

703 
205 

703 
215 

/ 


8.  If  Robert  picks  324  apples  and  Jack  picks  187,  how 
many  more  apples  does  Robert  pick  than  Jack  ? 

9.  In  a  city  school  of  523  pupils  267  are  girls.    How 
many  pupils  are  boys  ? 

10.  It  is  660  ft.  around  a  running  track.  After  a  boy 
has  run  480  ft.  of  this  distance,  how  much  farther  must 
he  run  to  go  all  the  way  around? 


70  SUBTRACTION 

ORAL  REVIEW  TEST 

Subtract  each  of  the  numbers  2,  3,  4,  S,  6,  7,  S,  and  9 
in  turn  from  each  of  the  folloioing  numbers  : 

1.  10  21  32  43  54  65  76  87  98 

2.  62  72  41  20  97  52  61  40  83 

3.  31  86  95  51  85  71  42  63  60 

4.  96  30  70  82  50  92  73  53  81 

5.  75  93  91  84  80  11  55  74  64 

WRITTEN  REVIEW  TEST 

Subtract  468  from  each  of  these  numbers : 
1.  512.  2.  601.  3.  725.  4.  836.  5.  957.- 

Subtract  379  from  each  of  these  numbers  : 
6.  425.  7.  536.  8.  648.  9.  717.        10.  800. 

Subtract  254  from  each  of  these  numbers : 
11.  506.        12.  521.        13.  632.        14.  703.        15.  812. 

Subtract  337  from  eojch  of  these  numbers : 
16.  425.        17.  502.        18.  616.        19.  723.        20.  900. 

Subtract  576  from  each  of  these  members : 
21.  841.        22.  723.        23.  900.        24.  811.        25.  612. 

Subtract  624  from  each  of  these  numbers : 
26.  721.        27.  712.        28.  801.        29.  813.        30.  900. 

If  the  check  is  insisted  upon,  it  will  give  a  review  of  addition. 


MULTIPLICATION  TABLES  BEGUN  71 

IV.  MULTIPLICATION  AND  DIVISION  TABLES 
ORAL  EXERCISE 

1.  Frank's  father  has  sent  him  to  buy  3  postage  stamps 
for  letters.  How  much  must  Frank  pay  for  each  stamp? 
How  much  must  he  pay  for  the  3  stamps  ? 

2.  How  much  is  2  +  2  ?   How  much  is  2  +  2  +  2  ?   How 

much  is  2  +  2  +  2  +  2? 

3.  If  Frank's  father  sends  him  for  4  postage  stamps  for 
letters,  how  much  money  must  he  give  him  ? 

4.  If  Frank's  father  has  5  letters  to  mail,  how  much  do 
the  stamps  cost  for  all  of  these  letters?  Which  is  better, 
to  add  2  +  2  +  2  +  2  +  2,  or  to  know  without  adding  how 
many  five  2's  are  ? 

5.  Frank  did  not  know  how  many  five  2's  are,  and  his 
father  told  him  to  count  by  2's,  hke  this :  2,  4,  6,  and  so 
on.  Then  Frank  found  how  many  five  2's  are.  How  many 
are  they? 

6.  How  many  are  three  2's  ?   How  many  are  four  2's  ? 

7.  Can  you  count  by  2's,  beginning  at  2  and  ending 
at  10  ?  Tiy  it. 

8.  Can  you  count  by  2's  to  12  ?  to  14  ?  to  18  ?  to  20  ? 
to  22  ?   Try  it. 

9.  Can  you  tell  how  much  Frank  would  have  to  pay  for 
ten  2^  stamps? 

It  is  advisable  to  introduce  real,  concrete  problems  of  this  nature  when 
a  new  subject  is  begun,  so  as  to  show  the  purpose  of  the  work.  These  prob- 
lems should  relate  to  the  home  or  school  interests  of  the  pupils. 


72 


MULTIPLICATION  AND  DIVISION  TABLES 


ORAL  EXERCISE 

1.  Add  the  columns  of  2's,  from  one  2  to  five  2's. 

2.  On  the  blackboard  and  on  paper  build  more  columns 
of  2's,  until  you  have  ten  2's  in  the 
last  column.   How  many  columns  are 
there  ? 

3.  Read  the  columns,  thus :  "  One 
2  is  2,  two  2's  are  4,  three  2's  are  6," 
and  so  on. 

4.  How  many  are  five  2's  ?  six  2's  ? 
seven  2's  ?  eight  2's  ?  nine  2's  ?  ten  2's  ? 

5.  Read  and  learn  this  table  of  2's,  thus :  "  Two  2's  are 
4  "  (or  else  "  two  times  2  are  4  "),  and  so  on : 

2x2  =  4  5x2  =  10  8x2  =  16 

3x2  =  6  6x2=12  9x2  =  18 

4x2  =  8  7x2=14  10x2=20 

6.  How  much  is  1x2?  2x1?  2x0?  0x2? 

7.  State  these  products : 

2x3      2x7      2x8      2x5 
2x6      2x4      2x9      2x10 

The  pupils  should  be  made  to  see  that  if  they  know  6x2,  they  also 
know  2x6;  therefore  these  inverse  drills  should  be  carried  right  along 
with  the  tables. 

8.  How  much  is  2  +  2  +  2?  3x2? 

9.  How  much  is  2  +  2  +  2  +  2?  4x2? 

10.  Read  and  learn :  11  x  2  =  22  ;  12  x  2  =  24. 


TABLE  OF  TWOS 


73 


ORAL  EXERCISE 

1.  At  2  cents  each,  how  much  will  3  tablets  cost? 

2.  At  2  cents  each,  how  much  will  4  pencils  cost  ? 

3.  At  2  cents  each,  how  much  will  7  papers  cost  ? 

At  2  cents  each,  find  the  cost  of  the  following : 

4.  5  penholders.  8.  9  postage  stamps. 

5.  8  spools  of  thread.  9.  4  pictures. 

6.  6  pears.  10.  9  calendars. 

7.  7  yards  of  braid.  11.  8  newspapers. 

If  S  X  ^  -\-l  is  equal  to  10  + 1,  state  the  values  of: 
12.5x2  +  3.  15.8x2  +  5.  18.6x2  +  1. 

13.  4  X  2  +  1.  16.  9  X  2  +  4.  19.  8  x  2  +  3. 

14.  3  X  2  +  1.  17.  7  X  2  +  3.  20.  5  x  2  +  4. 

This  carrying  drill  is  of  great  importance  in  multiplication. 
WRITTEN  EXERCISE 

Multiply  the  following : 


1.  2 

2 

4 

2 

2 

2 

1 

9 

0 

2 

2 

4 

2 

6 

8 

9 

3 

2 

2 

0 

2.  2 

3 

2 

5 

2 

6 

1 

2 

7 

8 

3 

2 

5 

2 

7 

2 

.    2 

1 

•2 

2 

3.  We  have  placed  here  2  rows  of  four  dots  each,  or  4 
coliuuns  of  2  dots  each.    This  shows  easily  that 
2x4  dots  =  4x2  dots.  Draw  12  small  squares, 
to  show  that  6x2  squares  =  12  squares,  and 
that  2x6  squares  =  12  sguares. 


•  •  •  • 


74 


MULTIPLICATION  AND  DIVISION  TABLES 


ORAL  EXERCISE 

1.  How  many  2's  do  you  see  in  4? 
How  many  2's  do  you  see  in  6  ? 

2.  How  many  2's  do  you  see  in  8  ? 
How  many  2's  do  you  see  in  10  ? 

3.  8  contains  2  how  many  times  ? 


Division.     The    answer   to  Ex,  3, 
"  8  contains  2  four  times,"  is  written 

8^2  =  4 


2 

2    2 

2 

2    2 

2 

2 

2    2 

2    2 

2 

2    2 

2    4 

6 

8  10 

2}8 
4 


In  each  case  8  is  called  the  dividend,  2  is  called  the 
divisor,  and  4  is  called  the  quotient. 

The  quotient  multijolied  hy  the  divisor  equals  the  dividend. 

The  quotient  is  sometimes  placed  above  the  dividend,  as  in  long  division, 
and  any  school  may  require  this  arrangement.  It  is  not,  however,  the  busi- 
ness custom,  and  it  is  inconvenient  in  some  advanced  work. 


4.  State  the  values  of  the  following : 
4x2  5x2  6x2 

2x4  2x5  2x6 

8-^2  10-2  12^2 

8-^4  10-5-5  12^6 

6.  Read  and  learn : 

4h-2  =  2  10^2  =  5 

6^2  =  3  12  ^2  =  6 

8h-2  =  4  14 -^2  =  7 


7x2 

2x7 

14-^2 

14  H- 7 

16^ 

-2=    8 

18 -^ 

■2=    9 

20 -^ 

■2  =  10 

TABLE  OF  THREES 


75 


ORAL  EXERCISE 

1.  Add  the  columns  of  3's,  from  one  3  to  five  3's. 

2.  On  the  blackboard  and  on  paper  build  more  columns 
of  3's,  until  you  have  ten  3's  in  the 
last  column.    How  many  columns  are 
there  ? 

3.  Read  the  columns,  thus:  "One 
3  is  3,  two  3's  are  6,  three  3's  are  9," 
and  so  on. 

4.  How  many  are  five  3's  ?  six  3's  ? 
seven  3's  ?  eight  3's  ?  nine  3's  ?  ten  3's  ? 

5.  Read  and  learn  the  table  of  3's,  thus :   "  Two  3's 
are  6  "  (or  else  "  two  times  3  are  6  "),  and  so  on. 

2x3=    6  5x3  =  15  8x3  =  24 

3x3=9  6x3  =  18  9x3  =  27 

.      4  X  3  =  12  7  X  3  =  21  10  x  3  =  30 

6.  How  much  islx3?3xl?3x0?0x3? 

7.  State  these  products : 

3x2  3x7  3x9  3x4 

3x3  3x5  3x6  3x8 

8.  How  much  is  3  +  3  ?   2  x  3  ? 

9.  How  much  is  3  +  3  +  3?    3x3? 

10.  How  much  is  3  +  3  +  3  +  3?   4x3? 


Complete  the  following: 


11.  2x 

=  6. 

13. 

x3=12. 

15.  2x3 

12.  3x 

=  9. 

14. 

x3=15. 

16.  7x3 

SP 


76         MULTIPLICATION  AND  DIVISION  TABLES 
ORAL  EXERCISE 

1.  Count  by  3's  from  3  to  36. 

2.  Repeat  the  multiplication  table  of  3's  to  10  x  3. 

3.  Read  and  learn : 

11  X  3  =  33  12  X  3  =  36 

State  the  answers  to  the  following : 

4.  4  X  3  + 1.  6.  5  X  3  +  2.  8.6x3  +  2. 

5.  7  X  3  +  5.  7.  8  X  3  +1.  9.  9  x  3  +  3. 

10.  How  much  is  3x0?  0x3?  2x0?  0x2? 

11.  If  1  orange  costs  3  cents,  how  much  will  6  oranges 
cost  ?  How  much  will  9  oranges  cost  ? 

12.  If  1  pencil  costs  3  cents,  how  much  will  7  pencils 
cost?  How  much  will  8  pencils  cost? 

13.  If  1  piece  of  burlap  used  in  making  a  carpet  for  a 
doll's  house  costs  3  cents,  how  much  will  8  pieces  cost  ? 

WRITTEN  EXERCISE 

Copy  and  complete  the  following : 

1.  4x=12  2x=6  x3  =  0 

2.  6  X     =  18  6  X     =  15  X  3  =  24 

3.  9  X     =  27  7  X     =  21  x  3  =  18 

4.  8  X     =  24  11  x     =  33  x  3  =  36 

5.  If  1  chair  costs  $3,  how  much  will  7  chairs  cost  ? 
How  much  will  9  chairs  cost? 

€.  If  1  school  desk  costs  $3,  how  much  will  12  school 
desks  cost?  How  much  will  11  school  desks  cost? 


TABLE  OF  THREES 


77 


ffRAL  EXERCISE 

1.  How  many  3's  do  you  see  in  6  ? 
How  many  3's  do  you  see  in  9  ? 

2.  How  many  3's  do  you  see  in  12  ? 
How  many  3's  do  you  see  in  15  ? 

3.  How  many  more  3's  are  there 
in  15  than  in  12  ? 

4.  State  the  values  of : 

4x3  5x3 

3x4  3x5 

12^3  15  H- 3 

12  H- 4  15-5 

5.  How  much  is  8x3?  3x8?  24  ^3?  24  ^8? 

6.  How  much  is  6x3?  3x6?  18-3?  18-6? 


3 

3    3 

3    3    3 

3 

3    3    3 

3    3 

3    3    3 

3    6 

9  12  15 

7x3 

9x3 

3x7 

3x9 

21-3 

27-3 

21-7 

27-9 

WRITTEN  EXERCISE 

1.  At  3^  each,  how  many  bananas  can  be  bought  for  9^ ? 
for  15(j^?  for24<^?  for30(^? 

2.  At  3  ^  each,  how  many  pencils  can  be  bought  for  12  ^  ? 
for  18(^?  for  21(^?  for  27(^? 

3.  At  3^  each,  how  many  oranges  can  be  bought  for  9^ 
and  12^  together? 

4.  How  many  threes  in  a  dozen  ?  in  a  half  dozen  ? 

5.  Copy  and  complete 


3  =  9 
3  =  7 


-3  =  6 
-3  =  5 


-  5  =  » 

-^-3  =  4 


78         MULTIPLICATION  AND  DIVISION  TABLES 
ORAL  EXERCISE 

1.  At  3^  each,  how  many  cakes  can  be  bought  for  12^? 
forl8(^?   for6(^?   for  9^?   for  15 <^? 

2.  If  3  sheep  cost  $24,  how  much  does  each  one  cost  ? 

3.  If  a  freight  train  goes  a  mile  in  3  minutes,  how  many 
miles  will  it  go  in  30  minutes  ? 

4.  A  yard  is  3  ft.  How  many  yards  in  30  ft.  ? 

5.  How  many  yards  of  braid,  at  3^  a  yard,  can  be  bought 
forl8(^? 

6.  If  you  need  27  sheets  of  paper  to  make  3  notebooks, 
how  many  sheets  will  you  need  for  1  notebook  ? 

7.  At  3^  each,  how  many  oranges  can  be  bought  for 
30<^?  for  21<^?  for  12(^?  for  18(^? 

8.  If  you  need  3  yd.  of  cloth  for  each  skirt,  how  many 
skirts  of  this  kind  can  you  make  from  27  yd.?  from 
18  yd.?   from  21  yd.?   from  12  yd.? 

WRITTEN  EXERCISE 

1.  Copy  this  table  and  learn  it : 

6^3  =  2  15^3  =  5  24^3=    8 

9-3  =  3  18-3  =  6  27-3=    9 

12 -3  =  4  21 -3  =  7  30-3  =  10 

Copy  and  complete  the  following : 

2.  9  ^     =  3.  5.  6  -^     =  3.  8.  12  -  2  = 

3.  12  ^     =  6.  6.  6  -     =  2.  9.  12  -  3  = 

4.  12  -     =  4.  7.  8  -4-  2  =  10.  21  -     =  7. 


TABLE  OF  FOURS 


79 


ORAL  EXERCISE. 

1.  Add  the  columns  of  4's,  from  one 
4  to  five  4's. 

2.  On  the  blackboard  and  on  paper, 
build  more  columns  of  4's,  until  you 
have  ten  4's  in  the  last  column. 
Then  read  the  columns,  thus:  "One  4 
is  4,  two  4's  are  8,"  and  so  on. 

3.  Read  and  learn  the  table  of  4's : 

2x4=    8  5x4  =  20 

3x4  =  12  6x4  =  24 

4x4  =  16  7x4  =  28 


8  X  4  =  32 

9  X  4  =  36 
10  X  4  =  40 


4.  How  much  is  1x4?   4x1?   4x0?   0x4? 

5.  How  much  is  4  +  4  +  4  +  4  +  4?   5x4? 

6.  State  these  products : 

4x3      4x8      4x9      4x7 
4x5      4x6      4x2      4x10 


WRITTEN  EXERCISE 

1.  There  are  4  quarts  in  1  gallon.    How  many  quarts  are 
there  in  5  gallons  ?   in  7  gallons  ?   in  9  gallons  ? 

2.  A  square  has  4  sides.    How  many  sides  have  8  squares  ? 

3.  A  cow  has  4  feet.    How  many  feet  have  2  cows? 
7  cows  ?   6  cows  ?   8  cows  ?   10  cows  ? 

4.  If  a  man  can  earn  $4  a  day,  how  many  dollars  can 
he  earn  in  9  da.?   in  7  da.?   in  8  da.? 


80 


MULTIPLICATION  AND  DIVISION  TABLES 


ORAL  EXERCISE 

1.  How  many  dots  are  there  in  each  of  these  squares? 
How  many  squares  are  there  in  the  upper  row?  How 
many  dots  are-  there  in  the 
squares  of  the  upper  row? 

2.  How  many  dots  are  there 
in  the  squares  of  the  lower 
row?  How  can  you  find  this 
without  adding  all  the  dots  in  the  squares  of  this  row? 

3.  How  many  squares  are  there  in  all?  How  can  you 
find  the  number  of  dots  without  adding  ?  How  many  dots 
are  there  in  all  ? 

State  the  answers  to  the  following : 

4.  5  X  4  +  1.              7.  8  X  4  +  3.  10.  3  x  4  +  2. 

5.  7  X  4  +  3.              8.  9  X  4  +  2.  11.  2  x  4  +  1. 

6.  6  X  4  +  2.              9.  4  X  4  +  3.  12.  8  x  4  +  2. 


WRITTEN  EXERCISE 

1.  There  are  4  stalks  of  com  in  a  hill.  How  many 
stalks  are  there  in  7  such  hills? 

2.  If  there  are  4  apples  in  each  of  9  groups,  how  many 
apples  are  there  in  all  the  groups  ? 

3.  How  many  shoes  does  it  take  to  shoe  3  horses?  to 
shoe  5  horses?   to  shoe  both  3  horses  and  5  horses? 

4.  One  man  has  3  horses  to  be  shod,  and  another  man 
has  4  horses  to  be  shod.  How  many  shoes  are  needed  for 
all  the  horses? 


TABLE  OF  FOUES 


81 


ORAL  EXERCISE 

1.  How  many  times  does  8  contain  4 

2.  How  many  4's  do  you  see  in  12  ?  i 

3.  How  many  times  does  16^  con- 
tain 4  (^?   20(^  contain  4  (^? 

4.  State  the  values  of : 

2x4           7x4           9x4 
4x2           4x7            4x9 
8-4         28-4         36-4 
8-2         28-7          36-9 

? 
n20 

?  inl6?  in4? 

4 
4 

4 

4    4 

4    4    4 

4    4    4    4 

4    4    4    4 

8  12  16  20 

5.  If  four  boys  have  equal  scores 
in  a  game  and  the  total  score  is  12,  what  is  each  score? 

6.  Read  and  learn  this  table : 

8-4  =  2  20-4  =  5  32-4=    8 

12-4  =  3  24-4  =  6  36-4=9 

16-4  =  4  28^4  =  7  40^4  =  10 


WRITTEN  EXERCISE 

1.  In  1  gallon  there  are  4  qt.    How  many  gallons  are 
therein  28  qt.?   in  36  qt.? 

2.  If  24  boys  are  marching,  4  in  a  line,  how  many  lines 
of  boys  are  there  ? 

Copy  and  complete : 

3.  24  -  4  =  16  ^     =  4  40  -  4  = 

4.  32-4=  28-     =7  36-4  = 


82 


MULTIPLICATION  AKD  DIVISION  TABLES 


ORAL  EXERCISE 

1.  Add  the  columns  of  5's,  from  one  5  to  five  5's. 

2.  On  the  blackboard  and  on  paper  build  more  columns 
of  5's  until  you  have  ten  5's  in  the 
last  column.    Then  read  the  columns, 
thus:   "One  5  is  5,  two  5's  are  10," 
and  so  on. 

3.  Read  and  learn  the  table  of  5's : 
2x5  =  10     5x5  =  25       8x5  =  40 
3x5  =  15     6x5  =  30       9x5  =  45 
4x5  =  20     7x5  =  35     10x5  =  50 

4.  How  much  is  1x5?   5x1?   5x0?  0x5?   5x5? 

5.  State  these  products : 

5x3      5x9      5x6      5x4 
5x7      5x2      5x8      5x10 


WRITTEN  EXERCISE 

1.  If  we  go  to  school  5  days  a  week  for  3  weeks,  how 
many  days  are  we  in  school  ? 

2.  If  it  costs  5^  to  telephone,  and  a  man  telephones  9 
times,  how  much  does  it  cost  him? 

3.  If  a  class  marches  in  rows  of  5,  and  there  are  7  rows, 
how  many  pupils  are  there  in  the  class  ? 

Copy  and  complete  the  following : 

4.  4x5  +  2=     6x5  +  3=     8x5  +  7  = 
'   5.9x5  +  7=     5x5  +  4=     3x5  +  2  = 


TABLE  OF  FIVES  83 

ORAL  EXERCISE 

1.  How  many  5's  are  there  in  5  ?  in  10  ?  in  15  ?  in  20  ? 
in  30  ?  in  45  ?  in  35  ?  in  50  ? 

2.  State  rapidly  the  results : 

40^5  30-5  15^5  35-^5 

3.  Read  and  learn  this  table : 

10-^5  =  2  25^5  =  5  40-5-5=    8 

15^5  =  3  30-^5  =  6  45h-6=9 

20  ^5  =  4  35 -^5  =  7  50  ^5  =  10 

4.  At  5^  each,  how  many  oranges  can  you  buy  for  20^? 
for  40(^?  for  25(^?  for  50*^? 

5.  At  $5  a  day,  how  many  days  must  a  man  work  in 
order  to  earn  $30  ? 

WRITTEN  EXERCISE 

Copy  and  complete  the  following : 

1.  35^       =7  ^5  =  4  15-5-5  = 

2.  45-       =9  -5  =  9  40-5  = 

3.  How  many  5-yard  lengths  can  be  made  from  45  yd. 
of  cloth  ?  from  35  yd.  ?  from  25  yd.  ? 

4.  At  5^  each,  how  many  oranges  can  you  buy  for  35^? 
for  45^?  forl5(^? 

5.  At  5^  each,  how  many  bottles  of  mucilage  can  you 
buy  for  40(^?  for  50(^?  for  20(^? 

6.  If  it  is  15  ft.  around  a  flower  bed,  and  each  side  ia 
5  ft.  long,  how  many  sides  are  there  ? 


84  MULTIPLICATION  AND  DIVISION  TABLES 

ORAL  REVIEW 

1.  There  are  2  boys  standing  by  each  of  6  desks.   How 
many  boys  are  standing  ? 

2.  There  are  2  girls  standing  by  each  of  8  desks.    How 
many  girls  are  standing  ? 

3.  There  are  2  pt.  in  a  quart.    How  many  pints  are 
there  in  9  qt.?   How  many  pints  are  there  in  10  qt.? 

4.  How  many  bananas  at  2^  each  can  you  buy  for  16^? 
How  many  bananas  can  you  buy  for  18^? 

5.  At  4^  each,  how  many  oranges  can  you  buy  for  12^? 
How  many  oranges  can  you  buy  for  32^? 

6.  If  you  have  20^,  how  many  oranges  can  you  buy  at 
3^  each,  and  how  much  money  will  you  have  left? 

WRITTEN  REVIEW 

1.  If  our  class  has  24  pupils  in  it,  and  they  march  in 
4  hues,  how  many  pupils  will  there  be  in  each  line  ? 

2.  If  there  are  27  boys  in  school,  how  many  baseball 
nines  can  be  formed  ? 

3.  If  you  buy  a  two-cent  stamp,  3  one-cent  stamps,  and 
a  one-cent  postal  card,  how  much  will  they  all  cost  ? 

4.  If  Mr.  Wood  earns  $3  a  day,  how  much  will  he  earn 
in  9  days  ? 

5.  If  Mr.  "Wood  earns  $3  a  day,  how  many  days  must 
he  work  to  earn  $24  ? 

6.  If  Mr.  Wood  has  $19  and  earns  $9  more,  how  much 
money  does  he  have  then  ? 


MULTIPLICATION 


85 


V.  MULTIPLICATION 


ORAL  EXERCISE 


Multiply  rapidly : 

1.  2345423523 
2452339395 


2.  4 

2 


How  to  Multiply.    If  you  have  23  marbles  and  John 
has  three  times  as  many,  how  many  marbles  has  John  ? 

To  multiply  23  by  3  we  see  that  3x3  ones  =  9  ones, 
and  we  write  the  9  below  the  line,  in  the  ones'  column. 

Then  3x2  tens  =  6  tens,  and  we  write  the 
6  below  the  line,  in  the  tens'  column. 
The  result  is  69,  so  John  has  69  marbles. 
23  is  called  the  multiplicand 

3  is  called  the  multiplier 
69  is  called  the  product 


23 
_3 

69 


WRITTEN  EXERCISE 


Multiply  the  following : 


1.  13 
2 

41 
2 

42 

2 

23 
2 

24 

2 

32 

2 

322 

2 

2.  21 
3 

31 
3 

22 

4 

11 

_4 

14 

2 

23 
_3 

231 
3 

86 


MULTIPLICATION 


ORAL  EXERCISE 

1.  Count  by  2's  from  2  to  20. 

2.  Recite  the  multiplication  table  of  2's. 

3.  Count  by  3's  from  3  to  30. 

4.  Recite  the  multiplication  table  of  3's. 

5.  Recite  the  multiplication  table  of  4's. 

Find  the  following  products : 

6.  7.  8.  9.  10.  11. 

21  51         63         52         41  63 

_2  _2  _2  _3  _4  J 

14.  Each  side  of  a  triangular  park  is  54  ft. 
long.  How  far  is  it  around  the  park  ?  Look  at 
this  multiplication  and  tell  what  is  the  product 
of  the  ones.  Tell  what  is  the  product  of  the 
tens.    Tell  what  is  the  whole  product. 

15.  In  Ex.  14,  what  way  do  you  see  of  mak- 
ing the  work  shorter  ? 


12. 

13. 

72 

81 

4 

5 

Further  Multiplication.    If  there  are  48  apple  trees  in 
each  of  4  rows,  how  many  trees  are  there  in  all? 

The  short  way  of  multiplying,  and  the  one 
which  we  should  always  use,  is  shown  here. 

We  see  that  4x8  ones  are  32  ones.  Write 
the  2  in  the  ones'  place  and  add  the  3  tens  to 
the  4x4  tens,  making  19  tens. 

The  product  is  192,  so  there  are  192  trees. 


ONE-FIGUEE  MULTIPLIER 


87 


ORAL  EXERCISE 

1.  At  8^  a  quart,  what  will  4  qt.  of  milk  cost? 

2.  How  much  is  2  x  8(^?  3  x  8^?  4  x  8^? 

3.  At  9(/!  each,  what  will  3  tablets  cost? 

4.  At  $7  each,  what  will  4  desks  cost? 

Multiply  the  following : 


5.  9 
3 

8 
4 

4 

7 

0 
3 

1 
3 

7 
4 

2 

9 

8 
2 

6.  3 

7 

6 
4 

0 
9 

1 

9 

8 
3 

4 
4 

7 
3 

9 
4 

WRITTEN  EXERCISE 


Multiply  the  following : 

1.  53  12  44  79 

4  5  7  2 


33 


22 
3 


222 
3 


2.  48 

4 

64 
4 

13 
5 

57 
3 

80 
4 

12 

4 

121 
4 

3.  34 
3 

55 
4 

75 

2 

24 
1 

68 
4 

32 

5 

322 
3 

4.  67 
2 

42 
7 

44 
8 

86 
3 

34 

9 

21 

4 

211 
4 

5.  89 
3 

78 
2 

56 
3 

31 
6 

97 
4 

63 
4 

231 
4 

88  MULTIPLICATION 

ORAL  DRILL  TEST.     ADDITION 


Add 

rapidly  : 

1.  12 

13 

14 

15 

17 

18 

19 

r 

0 

4 

5 

6 

3 

7 

8 

2.  23 

24 

25 

26 

27 

28 

29 

4 

5 

7 

5 

7 

9 

6 

3.  32 

33 

34 

45 

56 

67 

88 

6 

2 

7 

8 

7 

9 

7 

4.  10 

20 

30 

51 

63 

75 

82 

6 

7 

8 

7 

8 

5 

8 

3 

4 

4 

2 

2 

9 

9 

ORAL  DRILL  TEST.     SUBTRACTION 

Subtract  rapidly : 

1.  18  17  15  25  25  35  75 

5  7  8  8  18  18  18 


2.  19 

29 

44 

53 

53 

73 

93 

_4 

14 

14 

4 

14 

14 

24 

3.  11 

31 

31 

31 

51 

70 

70 

5 

5 

15 

25 

25 

20 

25 

4.  17 

37 

57 

52 

51 

61 

71 

12 

12 

22 

22 

22 

22 

23 

DRILL  TESTS  89 

ORAL  DRILL  TEST.     MULTIPLICATION 

Multiply  rapidly : 

1.  2  X  2.  8.  3  X  2.  15.  3x6.  22.  4  x  9. 

2.  2  X  6.  9.  3  X  8.  16.  4  x  5.  23.  5x2. 

3.  2x7.         10.  3x3.  17.  3  X  7.  24.  6x5.- 

4.  2x9.         11.  4x6.  18.  4  X  8.  25.  5x3. 

5.  2x8.         12.  4x7.  19.  3  X  5.  26.  5x4. 

6.  2x5.         13.  4x4.  20.  5  X  5.  27.  8x5. 

7.  2  X  10.       14.  3  X  10.         21.  4  x  10.         28.  5  x  10. 

State  rapidly  the  answers : 

29.  8  X  2  +  1.  33.  5  X  3  +  2.  37.  6  x  4  +  3. 

30.  7  X  3  +  1.  34.  4  X  3  +  1.  38.  8  X  5  +  4. 

31.  9  X  2  +  1.  35;  6  X  2  +  1.  39.  9  X  4  +  2. 

32.  6  X  3  +  2.  36.  7  X  5  +  4.  40.  7  x  5  +  3. 

ORAL  DRILL  TEST.     DIVISION 


Divide  ra 

pidly : 

1.  8^2. 

9. 

9^3. 

17. 

12^4. 

25. 

25^5 

2.  6^3. 

10. 

30-^3. 

18. 

30^5. 

26. 

36^4 

3.  6  H-  2. 

11. 

27-*- 3. 

19. 

16  H- 4. 

27. 

40-*- 5 

4.  16  H- 2. 

12. 

18-^3. 

20. 

10^5. 

28. 

50-*- 5 

5.  20-5-2. 

13. 

24-*- 3. 

21. 

20-*- 4. 

29. 

32-^4 

6.  18 -f- 2. 

14. 

15-*- 3. 

22. 

35-*- 5. 

30. 

45^5 

7.  12 -f- 2. 

15. 

21-*- 3. 

23. 

15^5. 

31. 

20-*- 5 

8.  10-*- 2. 

16. 

12-*- 3. 

24. 

24^4. 

32. 

28^4 

90 


USING  WHAT  YOU  HAVE  LEARNED 


VI.  USING  WHAT  YOU  HAVE  LEARNED 


NUMBERS  USED  IN  PLAY 

1.  If  each  of  these  three  boys  has  17  marbles,  how  many 
marbles  have  they  in  all  ? 

2.  If  each  of  the  three  boys  should  buy  12  more  marbles, 
how  many  more  marbles  would  they  all  have  ? 

3.  If  each  of  the  three  boys  has  34  marbles,  how  many 
marbles  do  they  all  have  ? 

4.  If  you  are  playing. a  game,  and  Fred*s  score  is  29  and 
your  score  is  twice  as  many,  what  is  your  score  ? 

5^  In  a  football  game  Jack's  team  scored  14  points  and 
Rob's  team  scored  this  number  multiphed  by  3.  How 
many  poiats  did  Rob's  team  score? 

6.  Mr.  "Wilson's  golf  score  was  88  and  Mr.  Brown's  was 
9  more.   How  much  was  Mr.  Brown's  score  ? 


PROBLEMS  91 

DRESSING  THE  DOLLS 

1.  Mollie  has  two  dolls.  One  cost  35(^  and  the  other 
cost  50^.    How  much  did  both  cost? 

2.  Mollie  bought  2  yd.  of  cloth  at  25^  a  yard  to  make 
dresses  for  her  dolls.    How  much  did  the  cloth  cost  ? 

3.  Mollie  bought  3  yd.  of  lace  for  the  dresses.  The  lace 
cost  12^  a  yard.    How  much  did  the  lace  cost  in  all? 

4.  A  doll's  necklace  was  made  by  stringing  beads. 
There  were  8  beads  to  an  inch.  How  many  beads  were 
there  in  5  in.  ?  How  many  were  there  in  2  in.  ?  How 
many  were  there  in  J  in.  ? 

5.  Mollie  uses  J  yd.  of  ribbon  for  sashes  for  her  dolls. 
The  ribbon  costs  16^  a  yard.  How  much  must  she  pay  for 
the  J  yd.  ?   How  do  you  find  i  of  16  ? 

6.  Mollie  uses  ^  yd.  of  ribbon  on  a  doll's  waist.  If  1  yd. 
costs  16^,  how  much  must  she  pay  for  the  J  yd.  ? 

7.  For  one  of  her  dolls  Mollie  buys  a  pair  of  shoes  for 
20^,  a  pair  of  stockings  for  5^,  a  skirt  for  15^,  and  a  hat 
for  25^.    How  much  does  she  pay  for  all? 

8.  Mollie  buys  4  strings  of  beads  for  trimming.  There 
are  48  beads  on  each  string.    How  many  beads  has  she  ? 

9.  Mollie  sees  some  strings  of  beads  that  the  store- 
keeper says  have  5  dozen  beads  on  a  string.  How  many 
beads  are  5  dozen  beads  ? 

10.  Make  a  list  of  things  for  two  dresses  for  a  doll,  and 
tell  how  much  you  think  they  would  cost. 

This  page  may  be  used  for  the  girls,  and  page  92  for  the  boys. 


92 


USING  WHAT  YOU  HAVE  LEAENED 


PROBLEMS  ABOUT  GAMES 

1.  Ralph  buys  a  baseball  mitt  for  50^  and  a  bat  for  30^. 
How  much  does  he  pay  for  both  ? 

2.  It  is  90  ft.  from  the  home  base  to  first  base,  and  90  ft. 
from  first  base  to  second.  How  far  does  Ralph  run  in  going 
from  home  base  to  first  base  and  then  to  second  base  ? 

3.  How  far  does  Ralph  run  in  making  a  home  run? 

4.  At  one  ball  game  in  the  school  grounds  there  were 
275  tickets  sold,  and  at  another  336  tickets.  How  many 
were  sold  for  the  two  games  ? 

5.  The  girls  played  bean-bag.  Jennie's  score  was  15, 
20,  18,  34.    What  was  her  total  score? 

6.  The  boys  played  ring  toss.  Jack's  score  was  12,  18, 
9,  17,  24.    What  was  his  total  score  ? 

7.  Fred  has  a  baseball  mitt  worth  75(^  and  John  has 
a  bat  worth  30^.  If  they  trade  fairly,  how  much  money 
should  John  give  Fred  in  addition  to  the  bat  ? 

8.  If  a  top  costs  6^,  marbles  5^  a  dozen,  and  a  ball  25^, 
how  much  will  a  top,  a  ball,  and  a  dozen  marbles  cost  ? 

9.  How  much  must  I  pay  for  24  marbles  at  5^  a  dozen  ? 

10.  Cut  nine  squares  of  paper  each 
small  enough  to  fit  in  one  of  these  little 
squares.  On  them  write  the  nine  figures 
1,  2,  3,  and  so  on  to  9.  Then  see  if  you 
can  put  them  in  these  squares  so  that  the 
sum  of  any  three  numbers  in  the  same 
row,  in  the  same  column,  or  in  the  same  diagonal  shall  be  15. 


DIVISION  93 

VII.  DIVISION 
ORAL  EXERCISE 

1.  How  do  you  find  half  of  4  ?  half  of  8  ?  half  of  12  ? 

2.  If  you  wish  to  find  one  fourth  of  8,  how  do  you  do  it  ? 

3.  If  Mary  has  24^  in  her  bank  and  spends  one  fourth 
of  it,  how  much  money  does  she  spend  ? 

4.  If  Mary  wishes  to  buy  |-  of  a  yard  of  cloth  that  costs 
160  a  yard,  how  much  money  must  she  spend? 

5.  Mary  buys  20  buttons  and  uses  one  fourth  of  them. 
How  many  does  she  use  ?   How  do  you  find  out  ? 

6.  If  Mary  has  24  hooks  and  eyes  and  uses  one  fourth 
of  them,  how  many  hooks  and  eyes  does  she  use? 

7.  Mary  bought  18  buttons  and  used  half  of  them.  How 
many  buttons  had  she  left? 

{j\  8.  If  Mary  has  28  in.  of  ribbon  and  cuts  it  into  pieces 
that  are  7  in.  long,  how  many  pieces  will  she  have  ?  How 
do  you  find  this  number  ? 

9.  If  Mary  should  have  84  in.  of  ribbon  and  should 
cut  it  into  pieces  that  are  7  in.  long,  how  would  you  find 
the  number  of  pieces  ?  Can  you  find  it  without  pencil  and 
paper  ?  Can  you  see  how  to  find  it  with  the  help  of  pencil 
and  paper  ? 

Teachers  will  at  once  see  that  this  exercise  is  intended  to  lead  up  to  the 
necessity  for  knowing  more  about  division.  Ex.  9  should  lead  the  pupil  to 
see  that  he  must  now  learn  something  new.  If  any  pupils  can  work  the 
example  already,  the  teacher  should  make  one  that  they  cannot  work.  In 
this  way  they  will  feel  the  necessity  for  further  study  of  division. 


94  DIVISION 

How  to  Divide.  John  has  48  marbles  and  Robert  has 
one  fourth  as  many.    How  many  marbles  has  Robert? 

We  see  that  we  must  divide  48  by  4. 

To  divide  48  by  4  we  write  the  numbers 
as  here  shown.  Then  4  tens  -^4  =  1  ten,  and 
we  write  the  1  in  the  tens'  place. 

Then  8  ones  -5-4  =  2  ones,  and  we  write  the  2  in  the 
ones'  place. 

The  quotient  is  12,  and  so  Robert  has  12  marbles. 

We  check  our  work  by  multiplying  the  quotient  by  the 
divisor.  If  the  product  equals  the  dividend,  the  work  is 
correct.   Here  4  x  12  =  48. 

WRITTEN   EXERCISE 

1.  Divide  by  2  ;  that  is,  find  J  of : 

24       28       42       48        66        82       84       844 

2.  Divide  by  3  ;  that  is,  find  J  of : 

33       36       60       69       39        96        66       666 

3.  Divide  by  4  ;  that  is,  find  J  of : 

44       40       80       88       84       24       48       444 

4.  Divide  63  by  3.    Make  a  problem  about  63-5-3. 

5.  There  are  88  apple  trees  in  4  equal  rows.  How  many 
apple  trees  are  there  in  each  row  ? 

6.  At  3^  each,  how  many  pencils  can  you  buy  with  36(^  ? 
ivith  63(^?  with  90(^?  P 

The  division  of  three-figure  numbers  should  grow  naturally  out  of  the 
-division  of  two-figure  numbers,  as  above. 


5)23 
4 
3  remainder 


KEMAINDER  IN  DIVISION  95 

Remainder  in  Division.  If  you  have  23  (^,  how  many 
oranges  can  you  buy  at  5(^  each,  and  how  much  money 
will  you  have  left? 

We  know   that  4  fives   are  20,   so 
23  -^  5  =  4,  and  there  is  3  left  over. 

So  we  see  that  we  can  buy  4  oranges, 
and  there  will  be  3^  left  over. 

We  say  that  23  is  not  exactly  divisi- 
ble by  5,  and  that  the  quotient  is  4  and  the  remainder  is  3. 

If  there  is  no  remainder,  the  division  is  said  to  be  exact, 

ORAL  EXERCISE 

State  rapidly  the  quotients  and  remainders : 

1.10^3.         3.32^3.  5.42^4.  7.41^5. 

2.  13^4.        4.  11-^3.  6.  25^3.  8.  47^4. 

WRITTEN  EXERCISE 

1.  At  5(^  each,  how  many  oranges  can  you  buy  with 
57 (^,  and  how  much  money  will  you  have  left? 

2.  At  4^  a  pound,  how  many  pounds  of  sugar  can  you 
buy  with  43^,  and  how  much  money  will  you  have  left? 

3.  At  2^  each,  how  many  postage  stamps  can  you  buy 
with  25 (^,  and  how  much  money  will  you  have  left? 

Divide,  giving  the  quotients  and  remainders : 

4.  45  ^  2.  7.  67  -  2.  10.  63  h-  2.  13.  81  -  2. 
5.35-3.  8.34-^3.  11.64^3.  14.  97 -^  3. 
6.  68  H- 3.        9.  94-^3.        12.  95-3.         15.  67-3. 


96  DIVISION 

Further  Work  in  Division.    If  one  orange  costs  3^,  how 
many  oranges  can  you  buy  with  57^? 

In  dividing  57  by  3  we  see  that  we  have 
5  tens  -^3  =  1  ten,  with  2  tens  left  over. 

We  write  the  1  in  the  tens'  place  in  the 
quotient,  below  the  5  tens. 

2  tens  +  7  ones  =  27  ones,  which  is  to  be  divided  by  3. 

27  ones  -5-3  =  9  ones,  and  we  write  the  9  in  the  ones' 
place,  below  the  7  ones. 

The  quotient  is  19,  and  so  you  can  buy  19  oranges. 

Check.   3x19  =  57. 

WRITTEN  EXERCISE 

1.  Divide  by  2  ;  that  is,  find  ^  of : 

32       34       52       58       72       96       44       448 

2.  Divide  by  3  ;  that  is,  find  ^  of : 

72       24       87       54       48       81       63       363 

3.  Divide  by  4  ;  that  is,  find  |-  of : 

56       52       64       72       96       92       36       364 

4.  At  4^  each,  how  many  oranges  can  you  buy  with  52^? 

Divide  the  following : 

5.  90  -^  3         84  ^  3         78  ^  3         57-3         993-3 

6.  88  -  4        84-4        93-3         76  h-  4         999  -^  3 

7.  If  the  dividend  is  75  and  the  divisor  is  3,  what  is  the 
quotient  ? 

8.  At  2^  each,  how  many  apples  can  you  buy  with  36^? 


FRACTIONS  97 

VIII.   FRACTIONS 
ORAL  EXERCISE 

1.  This  circle  has  been  divided  into  how  many  equal 
parts  ? 

2.  Each  of  these  equal  parts  is  called  what 
part  of  the  circle  ? 

3.  If  a  hne  is  divided  into  three  equal  parts, 
each  is  what  part  of  the  line  ? 

4.  What  is  one  of  the  three  equal  parts  of  anything 
called  ?   What  does  -J-  of  a  circle  mean  ? 

5.  There  are  three  feet  in  a  yard.    Then  1  foot  is  what 
part  of  a  yard  ? 

6.  What  is  meant  by  J  ?   by  J  of  a  dozen  ? 

7.  How  much  is  -J  of  3  in.  ?   ^  of  3  pounds  ? 

8.  How  long  is  a  line  that  is  J  of  a  Hne  3  ft.  long? 

WRITTEN  EXERCISE 

1.  Draw  a  line  3  in.  long  and  mark  off  ^  of  it. 

2.  Draw  a  line  1  in.  long.    Then  extend  the  line  so  that 
it  is  I"  in.  longer.    Mark  off  ^  of  the  whole  hne. 

3.  Here  are  6  stars  arranged  in  3  equal  groups.     *  *  * 
How  many  stars  are  J  of  6  stars  ?  *  *  * 

4.  Draw   9   stars  and   separate  them  into  three  equal 
groups.   How  many  stars  are  ^  of  9  stars? 

5.  Draw  12  stars  and  separate  them  into  2  equal  groups. 
How  many  stars  are  ^  of  12  stars  ? 


98 


FEACTIONS 


ORAL  EXERCISE 


1.  Block  B  is  how  many  times  as  large  as  (7?  Then  O 
equals  what  part  of  ^  ? 


2.  Block  A  is  how  many  times  as  large  as  (7?   Then  C 
equals  what  part  of  A  ? 

.     3.  K  C  weighs  1  pound,  how  many  pounds  does  5  weigh  ? 
If  B  weighs  1  pound,  how  many  pounds  does  C  weigh  ? 

4.  If  C  weighs  1  pound,  how  many  pounds  do  A  and  B 
together  weigh  ? 

5.  If  5  weighs  1  pound,  how  many  pounds  do  A  and  0 
together  weigh  ? 

6.  If  C  is  1  foot  high,  how  many  feet  high  is  J.  ?   If  ^  is 
1  foot  high,  how  high  is  C? 

7.  Is  C  more  or  less  than  half  of  J.?    Then  which  is 
greater,  J  or  ^  ? 

WRITTEN  EXERCISE 

Copy  and  complete : 

1.  i  +  i=  3.  J-J  = 

2.  J  +  i  +  i=  4.  l-i  = 


5.  J  of  6  - 

6.  I  of  9  = 


EELATIVE  SIZES 
ORAL  EXERCISE 

1.  Which  block  is  5  times  as  large  as  jE^? 

2.  Which  block  is  J-  (one  fifth)  as  large  as  J.  ? 


99 


C  D 

3.  Point  to  a  block  that  is  f  as  large  as  A. 
Point  to  blocks  as  follows: 

4.  |-  as  large  as  A.  6.  f  as  large  as  O. 

5.  |-  as  large  as  J..  7.  f  as  large  as  B. 

8.  If  we  call  A  one,  what  shall  we  call  El  D1  CI  B1 

9.  If  we  call  B  one,  what  shall  we  call  J/?  Z>?   (7? 

10.  Using  blocks  B,  C,  B,  and  U,  show  that  J  +  J-  =  J? 
and  that  J  +  J-  =  J- 

WRITTEN  EXERCISE 

1.  Draw  a  line  10  inches  long  and  another  2  inches  long. 
The  2-inch  line  is  what  part  as  long  as  the  10-inch  hne  ? 

2.  Draw  a  line  J  as  long  as  the  10-inch  hne. 

3.  Draw  a  hne  ^  as  long  as  the  10-inch  line.   It  is  how 
many  inches  long  ? 


100 


FRACTIONS 
ORAL  EXERCISE 


1.  If  we  divide  a  circle  into  thirds  and  cut  each  third 
into  halves,  how  many  equal  parts  are  there?  What  is 
each  part  called  ?   How  many  sixths  of  a  circle  in  1  circle  ? 


2.  Mary  gave  |-  of  a  pie  to  Juha,  ^  to  Ruth,  and  ^  to 
John.   How  many  sixths  did  she  give  away  ? 

3.  John's  mother  gave  him  J  of  a  pie  and  he  gave  ^  of 
his  piece  to  Ray.    What  part  of  the  pie  did  Ray  receive  ? 

4.  Show  ^  of  this  oblong ;  ^  of  it.   ^  is  what  part  of  J  ? 
■J-  =  how  many  sixths  ? 


^  =  how  many  sixths  ? 

Then  J  +  J  =  how  many 

sixths  ?     1^  +  ^  =  how  many  sixths? 

sixths  ? 

WRITTEN  EXERCISE 


-feFii 


M 


1  +  i-  =  how  many 


1.  This  oblong  shows  that  1  —  l  =  f.   Draw  nine  more 
oblongs  hke  this  one  and  shade  them  to  show  the  following: 


-^6         6 

1  —  1  =  ^ 


*  =  * 
f  =  * 


1  +  1  =  1 
6^6         3 

f  +  i  =  i 
i  +  i  =  i 


■ 

2.  Draw  an  oblong  6  inches  long  and  1  inch  wide.   Draw 
other  oblongs  ^,  J,  ^,  ■§-,  and  |-  as  long. 


FRACTIONAL  PARTS  101 

ORAL  EXERCISE 

1.  Draw  on  the  blackboard  a  line  1  foot  long  and  divide 
it  into  thirds.   Divide  each  third  into  halves.  Then 

J  is  what  part  of  |-  ?         f  are  how  many  sixths  ? 

2.  Point  to  J  of  the  line.    What  is  J-  of  ^  of  the  line? 

3.  How  many  sixths  of  a  foot  are  there  in  J  of  a  foot  ? 
in  1^  of  a  foot  ?   in  l  of  a  foot? 

4.  How  many  sixths  are  there  in  2  ?   in  21  (2  and  J-)  ? 

5.  Howmany  sixths  are  f-l?  1-^-?  f-J?  l-J? 

l_i?    1_4?    1—2.?    1  —  3.?    l_i? 

ORAL  EXERCISE 

1.  Draw  a  line  1  ft.  long.    Divide  it  into  halves.    How 
many  inches  are  there  in  ^  of  a  foot  ? 

2.  Divide  the  line  into  fourths.    How  many  inches  are 

there  in  J  of  a  foot?     , i 12 

in  I  of  a  foot?  ^ 

3.  How  many  fourths  4 

of  a  foot  are  there  in  -1-    ( 1 1 1 A 

3 
of  a  foot  ? 

I ! I ! I I 16. 

4.  Divide  the  line  in-  ® 
to  thirds.  How  many  inches  in  ^  of  a  foot  ?  in  |-  of  a  foot  ? 

5.  Divide  the  line  into  sixths.    How  many  inches  are 
there  in  i  of  a  foot  ?   in  |-  of  a  foot  ?   in  |-  of  a  foot  ? 

6.  How  many  sixths  are  there  in  i  ?   in  f  ?   in  -I  ? 

7.  Draw  a  line  10  inches  long  and  divide  it  into  fifths. 
Divide  it  into  tenths.    How  many  tenths  are  there  in  J? 


102  GENERAL  REVIEW 

IX.   GENERAL  REVIEW 
WRITTEN  EXERCISE 

Add  the  following : 


1.  123 

183 

189 

286 

474 

239 

472 

472 

472 

493 

298 

348 

2.  392 

286 

758 

538 

398 

456 

489 

509 

177 

269 

477 

481 

3.  287 

568 

429 

377 

522 

277 

387 

296 

492 

478 

398 

643 

4.  249 

287 

488 

526 

'  485 

298 

393 

573 

296 

375 

275 

437 

Subtract  the  following : 

5.  586 
231 


6. 

428 

169 

7. 

722 

434 

8. 

654 

278 

9. 

500 

417 

526 

581 

521 

562 

691 

231 

236 

236 

375' 

493 

532 

631 

741 

921 

907 

274 

227 

268 

329 

659 

653 

917 

642 

753 

811 

346 

289 

485 

368 

298 

716 

723 

820 

620 

923 

257 

334 

216 

325 

475 

600 

632 

704 

800 

710 

522 

333 

650 

488 

296 

GENERAL  EEVIEW 


103 


Multiply  the  following . 

10.  25 

33 

14 

24 

30 

33 

2 

2 

2 

3 

3 

3 

11.  41 

23 

40 

32 

43 

27 

3 

4 

j4 

4 

5 

_5 

12.  22 

31 

21 

42 

20 

59 

5 

5 

6 

6 

6 

2 

13.  34 

44 

33 

50 

45 

76 

7 

7 

8 

8 

9 

3 

14.  If  there  are  23  pupils  in  each  of  4  classes,  how  many 
pupils  are  there  in  all  ? 

15.  If  one  pupil's  desk  costs  a  school  $3,  how  much  will 
24  desks  cost  the  school  ? 

Remember  that  24  x  3  =  3  x  24. 

Multiply  each  of  the  numbers  4,  7, 8, 3,  S,  9, 6, 2,  in  turn : 

16.  By  3,  and  add  2  to  the  product. 

17.  By  4,  and  add  3  or  2  to  the  product. 

18.  By  5,  and  add  4,  3,  or  2  to  the  product. 

The  teacher  should  direct  the  number  to  be  added  each  time.    The  num- 
bers to  be  multiplied  should  be  written  on  the  blackboard. 


Divide  the  following : 

19.  By  2 

32 

42 

52 

62 

73 

75 

20.  By  3 

51 

57 

69 

75 

80 

91 

21.  By  4 

48 

56 

72 

81 

87 

93 

22.  By  5 

65 

75 

72 

83 

95 

99 

104 


USING  WHAT  YOU  HAVE  LEARNED 


X.  USING  WHAT  YOU  HAVE  LEARNED 
HOW  THE  COUNTRY  BOY  AND  GIRL  USE  THEIR  ARITHMETIC 

1.  Frank's  father  has  an  orchard  with  5  rows  of  apple 
trees,  17  trees  in  each  row.    How  many  trees  are  there? 

2.  Frank  picked  2  bushels  of  apples  from  each  of  the 
17  apple  trees.    How  many  bushels  did  he  pick  in  all  ? 


3.  Frank's  father  sold  2  bushels  of  apples  at  45^  a 
bushel.   How  much  did  he  receive  for  these  apples? 

4.  He  paid  Frank  5^  a  bushel  for  picking  apples.  After 
picking  15  bushels  how  much  money  had  Frank  earned  ? 

5.  If  Frank's  father  gave  him  4  hens,  and  Spot  laid 
7  eggs,  Black  Foot  6  eggs.  Fussy  8  eggs,  and  Browny 
9  eggs,  how  many  eggs  did  they  all  lay? 


GENERAL  REVIEW  105 

6.  After  Frank  had  3  dozen  eggs  he  sold  them  for  28(^ 
a  dozen.   How  much  money  did  he  receive  ? 

7.  If  Frank  has  62^  and  it  costs  him  25^  to  get  into 
the  fair,  how  much  does  he  have  after  buying  his  ticket  ? 

8.  Has  Frank  money  enough  left  (see  Ex.  7)  to  take  his 
sister  to  the  fair?   If  so,  how  much  would  he  have  left? 

9.  Mary  learned  to  milk  the  cows.  Her  father  paid 
her  by  giving  her  the  milk  from  one  of  the  cows.  This 
cow  gave  14  qt.  of  milk  a  day,  and  Mary  sold  this  to  a 
neighbor  at  5^  a  quart.    How  much  did  Mary  earn  a  day? 

10.  If  Mary  saves  16^  a  week,  how  much  money  does 
she  save  in  5  weeks? 

11.  Mary  is  saving  money  for  a  concert.  She  wishes  to 
take  her  aunt  and  cousin.  Her  aunt's  ticket  will  cost  50^, 
and  the  tickets  for  her  cousin  and  herself  will  cost  25^ 
each.    How  much  must  she  save  for  all  three  tickets? 

12.  If  Mary  picks  14  qt.  of  berries  and  sells  them  for 
3^  a  quart,  how  much  money  does  she  receive? 

13.  Mary's  mother  sends  her  to  town  with  her  father, 
and  tells  her  to  buy  4  yd.  of  calico.  Mary  finds  that  she 
must  pay  13^  a  yard  for  the  kind  she  needs.  How  much 
will  it  cost? 

14.  If  Mary  owes  the  storekeeper  52^  and  gives  him  a 
dollar,  how  much  change  does  she  receive? 

15.  Mary's  father  buys  a  mowing  machine  for  $65.  He 
pays  $48  down  and  asks  Mary  if  she  can  tell  how  much 
more  he  must  pay.    What  should  she  tell  him? 


106 


USING  WHAT  YOU  HAVE  LEARNED 


16.  Frank  and  his  cousin  made  a  snow  fort.  They  rolled 
6  snowballs  for  the  lowest  row,  6  for  the  next,  and  6  for 
the  top  row.  How  many  snow- 
balls did  they  use  for  the  front 
of  the  fort  ? 


17.  For  each  of  the  two  sides 
they  used  2  snowballs  in  each 
row.  How  many  snowballs  did  they  use  on  each  side? 
How  many  did  they  use  on  both  sides?  How  many  did 
they  use  for  the  whole  fort? 

18.  For  the  snow  fight  Frank  made  4  doz.  snowballs, 
and  his  cousin  made  3  doz.  How  many  snowballs  did 
each  make?   How  many  did  they  make  together? 

19.  Frank  coasted  on  his  sled  428  ft.,  and  his  cousin 
coasted  35  ft.  farther.    How  far  did  his  cousin  coast  ? 

20.  Frank  spent  5  min.  in  fixing  his  skates,  and  skated 
25  min.  Then  he  stopped  6  min.  to  fix  his  skates  again. 
He  skated  18  min.  more  and  then  went  home.  How  many 
minutes  was  he  skating  and  fixing  his  skates  ? 

Omit  Exs.  16-20  if  the  subjects  are  not  familiar  to  the  pupils. 

21.  Frank's  father  drove  to  town  on  Monday  with  16 
bushels  of  potatoes.  On  Tuesday  he  drove  in  with  18  bushels, 
and  on  Wednesday  with  14  bushels.  How  many  bushels 
did  he  take  to  town  on  these  three  days  ? 

22.  Frank  lives  4  miles  from  town.  How  many  miles 
does  his  father  drive  in  going  to  town  and  back?  How 
many  miles  did  he  drive  in  the  three  days? 


ORAL  TIME  TESTS 
ORAL  TIME  TEST  IN  MULTIPLICATION 

State  the  following  products : 

1.  4  X  5.  6.  3  X  3.  11.  9x5. 

2.  7  X  3.  7.  5  X  4.  12.  4x3. 

3.  8  X  2.  8.  6  X  5.  13.  6x2. 

4.  6  X  4.  9.  7  X  2.  14.  3x4. 

5.  5x5.  10.  9x2.  15.  8  X  4. 


107 


16.  9x4. 

17.  8x5. 

18.  3x2. 

19.  7x5. 

20.  8x3. 


State  the  results  of  the  following : 

21.  6  X  3  4-  2.  24.  5  X  2  +  1.  27.  3  x  4  +  1. 

22.  9  X  2  +  1.  25.  2  X  5  +  1.  28.  4  x  4  +  3. 

23.  3  X  5  +  2.  26.  8  X  3  +  2.  29.  9  x  5  +  4. 

The  results  of  these  29  examples  should  be  stated  in  2  minutes  or  less. 


ORAL  TIME  TEST  IN  DIVISION 


State  the  following  quotients : 


1.  9^3. 

2.  5^5. 

3.  6^1. 

4.  18^3. 

5.  20  H-  2. 

6.  50  ^  5. 

7.  45  H-  5. 

8.  36-4-4. 

9.  27^3. 


10.  4-4. 

11.  4h-2. 

12.  16^4. 

13.  35-5. 

14.  24-3. 

15.  32-4. 

16.  20-5. 

17.  15-3. 

18.  12-3. 


19.  3-3. 

20.  6-2. 

21.  21  -  3. 

22.  16-2. 

23.  30-5. 

24.  24-4. 

25.  25-5-5. 

26.  10-5-5. 

27.  30  -  3. 


28.  6-J- 

29.  2- 

30.  8- 

31.  18- 

32.  20 

33.  28- 

34.  10- 

35.  12- 

36.  10- 


The  results  of  these  36  examples  should  be  stated  in  1^  minutes  or 


3. 
2. 
4. 

^2. 
-4. 
^4. 
^1. 
4-4. 
^2. 

less. 


BP 


108  LITTLE  EXAMINATIONS 

XI.   LITTLE  EXAMINATIONS 
I. 


II. 


III. 


lY. 


V. 


1. 

9  +  37. 

5. 

28-^4. 

9. 

1  of  636. 

2. 

50-4. 

6. 

3x42. 

10. 

i  of  364. 

3. 

XI  =  (?). 

7. 

7x32. 

11. 

5qt.  =  (?)pt. 

4. 

5x4  +  2. 

8. 

56  H- 4. 

12. 

8pt.  =  (?)qt. 

1. 

7  +  45. 

5. 

24^3. 

9. 

1  of  36. 

2. 

45-7. 

6. 

24  ^  4. 

10. 

1  of  36. 

3. 

IX  =  (?). 

7. 

3x24. 

11. 

1  of  360. 

4. 

7x3  +  6. 

8. 

8x24. 

12. 

3ft.  =  (?)in. 

1. 

8  +  56. 

5. 

36^4. 

9. 

1  of  72. 

2. 

56-8. 

6. 

30-^3. 

10. 

iof72.     . 

3. 

VIII=(?). 

7. 

4x36. 

11. 

i  of  72. 

4. 

5x2  +  4. 

8. 

4x63. 

12. 

2yd.  =  (?)ft. 

1. 

6  +  49. 

5. 

32-^4. 

9. 

1  of  32. 

2. 

52-7. 

6. 

27^3. 

10. 

1  of  312. 

3. 

VII  =  (?). 

7. 

4x32. 

11. 

1  of  324. 

4. 

9x4  +  7. 

8. 

8x32. 

12. 

6ft.  =  (?)yd. 

1. 

7+58. 

5. 

240  -  4. 

9. 

1  of  124. 

2. 

57-8. 

6. 

240  H-  2. 

10. 

i  of  124. 

3. 

2  x  57. 

7. 

240  ^  3. 

11. 

1  of  123. 

4. 

3  X  57. 

8. 

2  X  240. 

12. 

lyd.  =  (?)in. 

These  Little  Examinations  at  the  close  of  each  chapter  furnish  excel- 
lent review  drill  work.  The  time  should  be  recordied  for  each,  and  the 
pupils  should  endeavor  to  improve  their  records. 


CHAPTER  m 

I.   READING  AND  WRITING  NUMBERS 


.. -.-rr  f*rA^?'r7! 


2000        +        300      +      40    +    2 


ORAL  EXERCISE 

1.  Ten  lOO's  make  one  thousand,  1000.  Count  by  lOOO's 
from  1000  to  10,000. 

2.  How  many  splints  are  there  in  the  pictm-e?  Write 
the  number  on  the  blackboard. 

3.  We  read  2000  thus:  "Two  thousand."  How  do  we 
read  3000  ? 

4.  We  read  2200  thus :  "  Two  thousand  two  hundred," 
or  "  twenty-two  hundred."  How  do  we  read  3200  ?  How 
do  we  read  4800? 

5.  We  read  2004  thus :  "  Two  thousand  four."  How 
do  we  read  3007?  3047?  3147?  5247? 

6.  Read  the  following  numbers  : 

27    270    2700    271    2710    2713 
35    350    3500    356    3560    3567 

109 


110  BEADING  AND  WEITING  NUMBERS 


ORAL  EXERCISE 

Read  the  following 

'  numbers : 

1.  1000. 

11. 

3000. 

21. 

5000. 

31. 

7000, 

2.  1200. 

12. 

3600. 

22. 

5005. 

32. 

7500, 

3.  1230. 

13. 

3670. 

23. 

5050. 

33. 

7596, 

4.  1235. 

14. 

3678. 

24. 

5055. 

34. 

8596. 

5.  1435. 

15. 

3996. 

25. 

6000. 

35. 

8798, 

€.  2000. 

16. 

4000. 

26. 

6600. 

36. 

9256, 

7.  2400. 

17. 

4040. 

27. 

6606. 

37. 

9398 

8.  2460. 

18. 

4004. 

28. 

6666. 

38. 

9872, 

9.  2465. 

19. 

4044. 

29. 

6756. 

39. 

9981, 

10.  2578. 

20. 

4444. 

30. 

6897. 

40. 

9999 

WRITTEN  EXERCISE 

Write  in  figures : 

1.  One  hundred  one ;  two  hundred  seven. 

2.  One  thousand  one ;  five  thousand  four. 

3.  Two  thousand  one  hundred  one. 

4.  Three  thousand  two  hundred  seven. 

5.  Three  thousand  four  hundred  seventeen. 

6.  Four  thousand  seven  hundred  sixty-five. 

7.  Five  thousand  five  hundred  fifty-five. 

8.  Six  thousand  eight  hundred  nineteen. 

9.  Seven  thousand  eight  hundred  ninety. 

10.  Nine  thousand  nine  hundred  ninety-nine. 

11.  Three  thousand  three  hundred  thirty-three. 


KOMAN  NUMERALS  111 

ORAL  EXERCISE 

1.  Read  these  numbers,  which  are  found  on  the  clock  face : 
III     IX     XII     I     VII     lY     XI     V     X     VI 

2.  Tell  the  time  when  the  minute  hand  points  to  XII 
and  the  hour  hand  points  to  IX ;  to  XI ;  to  II ;  to  X ;  to 
XII;  toIIII;  to  I;  to  VI ;  to  VII. 


Use  of  Roman  Numerals.  The  Roman  numerals  are  often 
used  for  numbering  the  chapters  of  books. 


1  to    5, 

I 

II 

III 

IV 

V 

6  to  10. 

VI 

VII 

VIII 

IX 

X 

11  to  15. 

XI 

XII 

XIII 

XIV 

XV 

16  to  20 

•      XVI 

XVII 

XVIII 

XIX 

XX 

3.  When  you  come  to  Chapter  XIV  in  a  book,  how 
many  chapters  have  you  read  ? 

4.  When  you  have  read  Chapter  IX  of  a  book  and  the 
last  chapter  is  XV,  how  many  chapters  have  you  to  read  ? 

WRITTEN  EXERCISE 

1.  Write  in  Roman  numerals  : 

15       8       11       17       13       9       6       10       14 

2.  Write  in  our  ordinary  numerals : 

XI     IX     XIX     XIV     XVII     VII     XVIII 

3.  Write  the  number  of  years  of  your  age,  both  in  ordi- 
nary numerals  and  in  Roman  numerals. 


112 


EEADING  AND  WRITING  NUMBERS 


ORAL  EXERCISE 

1.  These  children  are  plajdng  store.  Jack  buys  20^  worth 
of  candy  and  gives  a 
quarterof  a  dollar.  How 
much  change  is  due  ? 

2.  Fanny  buys  10^ 
worth  of  bananas  at  2 
for  a  nickel.  She  buys 
how  many  bananas  ? 

3.  The  dealer  says 
that  oranges  are  sold 
at  3  for  a  dime.  How 
much  will  half  a  dozen 
oranges  cost  ? 

4.  At  4(^  each,  how  much  will  3  oranges  cost  Fanny? 


Writing  Money.    In  writing  dollars  and  cents  we  write 
$2.50  for  2  dollars  and  50  cents, 
$15.05  for  15  dollars  and  5  cents, 
and  $0.75,  $.75,  or  75 (^  for  75  cents. 

Write  first  the  dollar  sign  ($),  then  the  number  of  dollars, 
then  a  period  {decimal  point),  and  then  the  number  of  cents. 

Both  $0.75  and  $.75  are  correct  forms  for  75  cents.  When  written  by 
itself,  $0.75  is  the  safer,  for  the  decimal  point  in  $.75  is  easily  overlooked  ; 
but  when  written  in  a  column,  as  in  addition,  there  is  no  need  for  the  0. 

The  teacher  should  also  allow  such  forms  as  75  ct.  and  75  c.  instead  of 
75^,  because  they  are  in  common  use  and  the  pupils  should  know  them. 

The  pupils  should  be  told  that  in  addition  and  subtraction  the  dollar 
sign  ($)  is  written  only  before  the  top  number  and  before  the  result. 


UNITED  STATES  MONEY 


iia 


ORAL  EXERCISE 

Read  the  following : 

1.  $1.25. 

9.  $19.05. 

17.  $231.00. 

25. 

$219.36, 

2.  $2.07. 

10.  $21.00. 

18.  $217.81. 

26. 

$246.95, 

3.  $3.00. 

11.  $32.01. 

19.  $329.75. 

27. 

$318.86, 

4.  $5.75. 

12.  $75.56. 

20.  $831.08. 

28. 

$981.99, 

5.  $4.00. 

13.  $65.00. 

21.  $106.75. 

29. 

$152.50, 

6.  $5.65. 

14.  $46.73. 

22.  $415.50. 

30. 

$524.25, 

7.  $5.50. 

15.  $36.75. 

23.  $142.80. 

31. 

$157.90, 

8.  $7.00. 

16.  $40.02. 

24.  $300.75. 

32. 

$423.86, 

WRITTEN  EXERCISE 

Write  in  figures,  with  the  proper  signs  for  money : 


1.  4  dollars 

2.  16  dollars 

3.  14  dollars 

4.  18  dollars 

5.  230  dollars 
8.  100  dollars 

7.  184  dollars 

8.  200  dollars 

9.  300  dollars 
10.  400  dollars 


1  dollar  and  75  cents 
3  dollars  and  3  cents 
7  dollars  and  25  cents 
16  dollars  and  80  cents 
175  dollars  and  75  cents 
248  dollars  and  49  cents 
250  dollars  and  49  cents 
600  dollars  and  50  cents 
750  dollars  and  85  cents 


286  dollars  and  98  cents 

11.  Seven  hundred  sixty-eight  dollars. 

12.  One  hundred  fifty  dollars  and  ten  cents. 

13.  Two  hundred  seventy-five  dollars  and  ten  cents. 


114 


ADDITION 


II.   ADDITION 

Adding  Long  Columns.  In  adding  long  columns  we  may 
write  the  sum  of  each  column  separately.  Business  men 
often  do  this.  We  may  add  up  the  first 
time,  and  check  the  result  by  adding  doivn. 

When  you  look  at  two  figures,  always 
think  of  the  sicm  of  the  two  numbers. 
Instead  of  saying  "  3  and  4  are  7,"  simply 
look  at  3  and  4  and  think  "  7." 

When  you  look  at  the  ones'  column  you 
should  see  the  two  lO's  (3  +  5  +  2,  and 
7  +  3)  at  once,  and  you  should  see  that 
the  sum  is  two  lO's  and  6,  or  26. 

Add  rapidly;  if  you  do  so,  you  will 
usually  make  fewer  mistakes. 

Uniting  two  or  more  numbers,  called  addends,  so  as  to 
make  a  single  number  is  called  addition. 

The  teacher  should  explain  that  the  sign  $,  written  before  the  first 
addend  in  a  column,  applies  to  all  addends  in  the  column. 


WRITTEN   EXERCISE 


Add  the  following : 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

42 

52 

29 

52 

48 

139 

$24 

28 

33 

71 

73 

78 

27 

36 

41 

48 

36 

81 

32 

53 

42 

79 

48 

64 

64 

52 

66 

33 

16 

67 

82 

75 

26 

53 

25 

ADDING  LONG  COLUMNS 


115 


ORAL  EXERCISE 


Add  from  the  bottom  to  the  top,  group  when  possible,  and 
check  the  work  by  adding  from  the  top  to  the  bottom : 


1. 
2 

4 
6 
5 

7 
9 


2. 

2 
3 
7 
6 
5 


3. 

8 
7 
3 
4 
9 
6 


4. 


5. 

8 
2 
5 
5 
7 
3 


6. 

2 
3 

4 
7 
6 
2 


7. 
8 
3 
6 

9 


8. 

3 

8 
2 
6 
9 


9. 

2 
4 
8 
3 
9 
6 


These  are  types  of  problems  to  be  written  on  the  board  for  rapid  drill 
•work. 

WRITTEN  EXERCISE 


A.dd,  checking  the  work  as  stated  above : 


1. 

2. 

3. 

4. 

5. 

23 

89 

37 

85 

81 

48 

64 

40 

23 

72 

72 

73 

29 

40 

35 

69 

29 

82 

27 

86 

43 

82 

76 

82 

92 

6. 

7. 

8. 

9. 

10. 

128 

834 

828 

828 

348 

932 

281 

204 

926 

492 

486 

342 

896 

349 

687 

629 

907 

480 

877 

402 

348 

602 

320 

492 

374 

726 

270 

981 

681 

200 

116.  .  ADDITION 

WRITTEN  EXERCISE 

1.  George  works  after  school  for  Mr.  Forbes,  the  grocer. 
Mr.  Forbes  set  him  at  work  sorting  oranges.  George  found 
196  good  oranges  in  one  box  and  188  in  another  box.  How 
many  good  oranges  did  he  find  in  both  boxes  ? 

2.  Mr.  Forbes  had  George  take  the  cans  of  fruit  from 
the  shelves  so  as  to  count  them.  He  counted  97  cans  of 
peaches,  86  cans  of  pears,  and  47  cans  of  plums.  How 
many  cans  were  there  of  all  three  kinds?      "  \ 

3.  George  arranged  some  cakes  of  soap  on  the  shelves. 
There  were  127  cakes  of  one  kind,  246  of  another,  and 
144  of  another.    How  many  cakes  of  soap  were  there  ? 

4.  George  polished  the  eating  apples  so  that  they  would 
sell  better.  He  polished  98  apples  of  one  kind,  139  of 
another,  and  74  of  another.  How  many  apples  did  he  pohsh? 

5.  Mr.  Forbes  paid  George  15^  on  Monday,  15^  on  Tues- 
day, 18^  on  Wednesday,  20^  on  Thursday,  15^  on  Friday, 
and  25^  on  Saturday.  How  many  cents  did  he  pay  him 
that  week  ? 

6.  Mr.  Forbes  put  |25  in  the  bank  on  Monday,  $35  on 
Tuesday,  $30  on  Wednesday,  $36  on  Thursday,  $45  on 
Friday,  and  $48  on  Saturday.  How  much  money  did  he 
put  in  the  bank  that  week  ? 

7.  Mr.  Forbes  spent  $35  one  day  and  $18  another  day. 
How  much  money  did  he  spend  altogether  ? 

8.  If  Mr.  Forbes  had  $250  in  the  bank,  and  then  put  in 
$75  more,  and  then  drew  out  $25,  how  much  money  was 
left  in  the  bank  ? 


COLUMN  ADDITION  117 

WRITTEN  EXERCISE 

Add,  timing  yourself: 


1. 

2. 

3. 

4. 

5. 

$217 

246 

276 

329 

$437 

343 

434 

427 

286 

293 

6. 

7. 

8. 

9. 

10. 

$127 

142 

326 

463 

$123 

246 

237 

293 

298 

247 

329 

421 

147 

127 

409 

11. 

12. 

13. 

14. 

15. 

106 

213 

106 

132 

222 

287 

129 

219 

167 

333 

109 

308 

137 

207 

111 

16. 

17. 

18. 

19. 

20. 

121 

106 

217 

272 

319 

42 

92 

102 

129 

107 

37 

37 

69 

106 

28 

168 

15 

72 

43 

63 

21. 

22. 

23. 

24. 

25. 

$136 

$127 

$147 

$192 

$400 

42 

38 

29 

37 

125 

81 

25 

108 

91 

30 

92 

172 

32 

82 

19 

237 

81 

129 

263 

16 

148 

69 

70 

109 

128 

118  ADDITION 

Addition  of  Money.  Ruth  put  $2.70  in  her  bank  in  one 
month,  $3.65  the  next  month,  and  $0.38  the  first  week  of 
the  following  month.  How  much  did  she  put 
in  the  bank  in  all  ? 

We  see  that  we  must  add  $2.70,   $3.65, 
and  $0.38. 

We  first  write  the  numbers  so  that  the  dec- 
imal points  are  under  one  another. 

Then  8  cents  +  5  cents  =  13  cents  =  1  dime 
-f  3  cents.    We  write  the  3  in  the  cents'  column  and  add 
the  1  to  the  dimes. 

Then  1  dime  +  3  dimes  +  6  dimes  +  7  dimes  =  17  dimes 
=  $1  +  7  dimes.  We  write  the  7  in  the  dimes'  column  and 
add  the  1  to  the  dollars. 

Then  $1  +  $3  +  $2  =  $6.  We  write  the  6  in  the  dollars' 
column  and  put  the  decimal  point  under  the  decimal  points. 

The  sum  is  $6.73,  so  Ruth  has  put  $6.73  in  her  bank. 

WRITTEN  EXERCISE 

Add  the  following ,  and  check  the  work : 


1. 

2. 

3. 

4. 

5. 

$4.83 

$4.89 

$5.90 

$5.96 

$8.92 

5.64 

5.66 

2.75 

2.78 

5.78 

6. 

7. 

8. 

9. 

10. 

$1.27 

$6.92 

$8.75 

$9.22 

$8.37 

3.87 

5.23 

5.68 

.76 

.98 

.25 

.35 

1.27 

2.60 

3.00 

COLUMN  ADDITION 


119 


WRITTEN  EXERCISE 

1.  Robert  helps  in  a  grocery  after  school,  and  the  grocer 
sometimes  sets  him  at  work  to  add  the  bills.  Mrs.  James 
has  bought  groceries  costing  $1.30,  $1.20,  $0.65,  and  $0.96. 
Robert  adds  these  amounts.    What  is  their  sum  ? 

2.  Robert  finds  that  Mrs.  Monroe  has  bought  groceries 
costing  $2,25,  $1.60,  $0.75,  $1.32,  $0.65,  and  $1.18.  How 
much  does  she  owe  ? 

The  grocer  gives  Robert  hills  with  the  following  items  to 
add.   Find  the  sum  of  each : 


3. 

4. 

5. 

6. 

7. 

$1.42 

$5.20 

$2.19 

$1.44 

$3.20 

.36 

3.60 

3.16 

3.00 

1.40 

.48 

4.32 

.42 

1.36 

.39 

.27 

.68  • 

3.27 

.42 

1.86 

3.62 

.49 

1.68 

1.07 

.42 

Rohert  finds  that  the  hills  are  usually  ruled.,  so  that  he 
does  not  have  to  write  the  dollar  sign  or  the  decimal  j^oint. 
He  finds  that  the  columns  look  like  this.    Add  each  hill: 


9. 


10. 


11. 


12. 


2 

10 

3 

15 

42 

1 

00 

38 

32 

1 

06 

3 

00 

3 

68 

46 

48 

72 

68 

49 

98 

1 

06 
73 

39 

87 

71 

96 

76 

98 

2 

96 
43 

120  SUBTRACTION 

III.    SUBTRACTION 
WRITTEN  EXERCISE 

Subtract,  timing  yourself  and  checking  the  work 


1. 

2. 

3. 

4. 

5. 

6. 

236 

342 

409 

527 

400 

326 

129 

273 

263 

329 

192 

178 

7. 

8. 

9. 

10. 

11. 

12. 

409 

600 

725 

908 

.   752 

360 

237 

482 

'  536 

809 

429 

290 

13. 

14. 

15. 

16. 

17. 

18. 

728 

342 

801 

712 

801 

902 

299 

139 

236 

348 

296 

327 

19. 

20. 

21. 

22. 

23. 

24. 

711 

628 

$426 

$304 

$322 

$209 

344 

439 

278 

265 

148 

168 

25. 

26. 

27. 

28. 

29. 

30. 

$387 

$400 

$925 

$305 

$492 

$286 

296 

275 

560 

197 

137 

192 

31. 

32. 

33. 

34. 

35. 

36. 

$840 

$927 

$209 

$325 

$430 

$535 

726 

109 

110 

186 

345 

287 

37. 

38. 

39. 

40. 

41. 

42. 

$415 

$523 

$816 

$927 

$862 

$900 

236 

475 

536 

349 

468 

521 

MAKING  CHANGE  121 

Making  Change.  If  you  owe  the  grocer  35^  and  give 
him  a  50-cent  piece,  he  makes  change  by  finding  the  amount 
which,  added  to  35^,  makes  50^.  He  does  this  by  saying, 
"35  and  5  are  40,  and  10  are  50,"  taking  up  5^  and  10^  as 
he  says  this.   He  then  gives  you  15^. 

If  the  school  is  provided  with  toy  money  it  should  be  used  at  this  time. 
The  drill  is  valuable  without  this,  however,  for  this  is  exactly  the  kind  of 
work  that  we  have  to  do  mentally  when  we  make  purchases. 

ORAL  EXERCISE 

1.  Make  change  for  50^,  when  you  owe : 

25^  30(^  40(^  45(^  29^  31(^ 

2.  Make  change  for  25^,  when  you  owe : 

20(fi  22(^  18^  15(^  9^  19^ 

3.  Make  change  for  75^,  when  you  owe : 

72(^  62(^  58(^  69(^  blf  67<^ 

4.  Make  change  for  $1,  when  you  owe : 

95(^  85(^  68(^  52(^  36(^  91^ 

75(^  80(^  55<^  65(^  20(^  25(^ 

5.  Mary  buys  some  ribbon  for  18  (^  and  gives  the  dealer 
25^.   How  much  change  is  due  ? 

6.  Rob  buys  a  ball  for  65(^  and  gives  the  dealer  |1. 
How  much  change  is  due? 

7.  Harriet'  buys  some  cloth  for  $1.20.  She  gives  the 
dealer  a  2-dollar  bill.    How  much  change  is  due? 


122  SUBTKACTION 

Subtraction  of  Money.    If  Mr.  Brown  has  $247.50  and 
spends  $176.75  of  it  for  some  cattle,  how 
much  money  has  he  left? 

We  see  that  we  must  subtract  $176.75 
from  $247.50. 

"We  write  the  numbers  as  here  shown. 

10  —  5  =  5.   We  write  the  5  under  cents. 

14  —  7  =  7.    We  write  the  7  under  the  dimes. 

We  now  write  the  decimal  point. 

6  —  6  =  0.    We  write  the  0  under  the  dollars. 

14  —  7  =  7.    We  write  the  7  under  the  tens  of  dollars. 

1  —  1=0,  so  there  are  no  hundreds  of  dollars. 

The  result  is  $70.75,  and  so  Mr.  Brown  has  $70.75  left. 

In  subtracting  United  States  money,  write  the  numbers  so 
that  the  decimal  points  are  in  a  column  and  subtract  in  the 
usual  way. 

WRITTEN  EXERCISE 


Subtract, 

and  check  the  work : 

1. 

$72.41 
24.92 

2. 

$29.84 
12.97 

3. 

$94.76 
76.98 

4. 

$60.70 
55.81 

5. 

$50.01 
20.09 

6. 

$65.42 
59.97 

7. 

$90.08 
25.19 

8. 

$52.86 
23.94 

9. 

$341.65 
120.40 

10. 

$341.65 
170.40 

11. 

$341.65      • 
170.46 

12. 
$341.65 
173.46 

UNITED  STATES  MONEY  123 


ORAL  EXERCISE 

Subtract  the  following : 


1. 

$3.60 
.10 

2. 

$3.09 
.04 

3- 

$3.69 
.14 

4. 

$3.65 
1.14 

5. 

$5.75 
2.14 

6. 

$5.95 
1.20 

T. 

$4.65 
1.10 

8. 

$5.55 
4.44 

9. 

$8.75 
.25 

$8.96 
1.96 

WRITTEN  EXERCISE 

Subtract,  check  the  loork,  and  time  yourself: 


1. 

2. 

8. 

4. 

5, 

$76.29 

$85.36 

$76.29 

$14.36 

$70.24 

75.37 

6.87 

62.89 

5.63 

10.65 

6. 

7. 

s; 

9. 

10. 

$96.73 

$88.41 

$95.27 

$33.42 

$47.63 

77.96 

79.52 

9.86 

9.29 

8.24 

11. 

12. 

13. 

14. 

15. 

$26.96 

$60.00 

$21.40 

$40.00 

$90.00 

17.27 

42.36 

17.52 

5.75 

36.27 

16. 

17. 

18. 

19. 

20. 

$24.00 

$32.09 

$41.32 

$68.03 

$75.00 

.78 

16.70 

28.75 

49.26 

.69 

124  MULTIPLICATION  AND  DIVISION 

IV.   MULTIPLICATION  AND  DIVISION 
ORAL  EXERCISE 

1.  Minnie  helps  her  mother  make  and  care  for  the 
flower  garden  at  their  home.  Minnie  has  planted  some 
violets,  6  plants  in  each  row.  How  many  plants  has  she 
in  2  rows? 

2.  But  Minnie  has  more  than  2  rows  of  plants ;  she  has 
4  rows.  How  do  you  find  the  number  of  plants  in  4  rows  ? 
How  many  plants  are  there  ? 

3.  If  Minnie  sets  out  2  more  rows,  she  will  have  6  rows 
in  all.  There  are  6  plants  in  each  row.  How  do  you  find 
the  number  of  plants  in  all  6  rows  ? 

4.  How  much  is  6  +  6  ?  How  much  is  6  +  6  +  6  ?  How 
much  is  6  +  6  +  6  +  6?  Which  is  easier,  to  add  these,  or  to 
find  the  answers  by  multiplying  ? 

5.  Howmuchis6  +  6?  12  +  6?  18  +  6?  24  +  6?  Count 
by  6's  from  6  to  30. 

6.  If  Minnie  sets  out  another  row  of  violets,  she  will  have 
7  rows,  and  there  will  be  6  plants  in  each  row.  How  do 
you  find  the  number  of  plants  in  all?  Is  it  easier  to  add 
6+6  +  6  +  6  +  6  +  6  +  6,  or  to  know  without  adding  how 
many  seven  6's  are  ?  Do  you  know  how  much  7  x  6  is  ?  If 
you  do  not  know,  how  can  you  find  out  ? 

The  pupil  is  now  about  to  begin  the  second  half  of  the  multiplication 
tables.  By  simple  examples  like  those  above  he  should  be  led  to  see  the 
advantage  of  learning  the  tables.  He  should  see  that,  although  he  could 
find  his  results  by  adding,  it  is  much  easier  and  quicker  to  use  the  mul- 
tiplication tables. 


TABLE  OF  SIXES 


125 


6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

ORAL  EXERCISE 

1.  Add  the  columns  of  6's,  from  one  6  to  five  6's. 

2.  On  the  blackboard  and  on  paper  build  more  columns 
of  6's,  until  you  have  ten  6's  in  the  last 
column.  How  many  columns  are  there  ? 

3.  Read  the  columns,  thus:  "One 
6  is  6,  two  6's  are  12,  three  6's  are 
18,"  and  so  on. 

4.  How  many  are  five  6's  ?  six  6's  ? 
seven  6's  ?  eight  6's  ?  nine  6's  ?  ten  6's  ? 

5.  Read  and  learn  this  table  of  6's, 

thus :  "  Two  6's  are  12, "  or  "  two  times  6  are  12, "  and 

so  on: 

2x6  =  12  5x6  =  30  8x6  =  48 

3x6  =  18  6x6  =  36  9x6  =  54 

4x6  =  24  7x6  =  42  10x6  =  60 

6.  How  much  is  1x6?  6x1?  6x0?  0x6? 

7.  How  much  is6  +  6  +  6?3x6? 

8.  How  much  is  6  +  6  +  6  +  6  +  6?  5x6? 

9.  State  the  values  of  the  following : 

2x6+1       3x6+2       5x6+1 
3x6+1       4x6+3       5x6+2 

10.  State  rapidly  the  following  products : 
6x1  6x8  6x4 

6x5  6x7  6x2 

1x6  8x6  4x6 

5x6  7x6  2x6 


6x3 
6x9 
9x6 
0x6 


126  MULTIPLICATION  AND  DIVISION 

One-Figure  Multiplier.  A  dealer  bought  6  automobiles. 
Including  freight,  they  cost  him  $807  each.  How  much 
did  they  all  cost? 

We  see  that  they  all  cost  6  x  $807. 

6x7  ones  =  42  ones  =  4  tens  +  2  ones. 
We  write  the  2  in  the  ones'  place  and  add 
the  4  to  the  tens. 

6x0  tens  =  0  tens ;  but  we  have  4  tens 
already  from  the  42,  so  we  write  the  4  in  the  tens'  place. 

6x8  hundreds  =  48  hundreds  =  4  thousands  +  8  hun- 
dreds. We  write  the  8  in  the  hundreds'  place,  and  the  4 
in  the  thousands'  place. 

The  product  is  4842,  and  so  the  automobiles  cost  $4842. 

Teachers  should  note  that  the  tables  thus  far  learned  are  sufficient  for 
any  multiplication  or  any  division  in  which  either  factor  is  less  than  6. 

WRITTEN  EXERCISE 

1.  How  many  "  week  days  "  are  there  in  31  weeks  ? 

2.  At  6^  a  pound,  how  much  will  21  lb.  of  sugar  cost? 

3.  At  $6  apiece,  how  much  will  30  lamps  cost  ? 

Multiply  the  following : 

4.  5.       6.       7.       8.       9. 
201     301     501     401     901     701 

6      6      6      6      6      6 

Copy  and  complete  the  following  : 

10.  5x6  +  3=     9x6  +  4=     6x6  +  4  = 

11.7x6  +  6=     8x6  +  3=     3x6  +  2  = 


ONE-FIGURE  MULTIPLIER 


127 


Multiplication  Continued.    "We  multiply  325  by  6  thus : 

6x5  ones  =  30  ones,  or  3  tens  and  0  ones.  We  write 
the  0  in  the  ones'  place  and  add  the  3  tens  to 
the  next  product. 

6x2  tens  =  12  tens,  and  12  tens  +  3  tens 
=  15  tens,  or  1  hundred  and  5  tens.  We  write 
the  5  in  the  tens'  place  and  add  the  1  hundred 
to  the  next  product. 

6x3  hundreds  =  18  hundreds,  and  we  know  that 
18  hundreds  + 1  hundred  =  19  hundreds,  or  1  thousand 
and  9  hundreds.  We  write  the  9  in  the  hundreds'  place 
and  the  1  in  the  thousands'  place. 

The  product  is  1950. 


WRITTEN  EXERCISE 


Multiply  the  following : 

1. 

2. 

3. 

4. 

5. 

6. 

120 

125 

234 

325 

425 

275 

2 

2 

2 

2 

2 

2 

7. 

8. 

9. 

10. 

11. 

12. 

320 

321 

325 

343 

446 

453 

3 

3 

3 

3 

3 

3 

13. 

14. 

15. 

16. 

17. 

18. 

206 

216 

265 

236 

326 

525 

4. 

5 

6 

7 

8 

9 

19. 

20. 

21. 

22. 

23. 

24. 

406 

461 

416 

466 

566 

728 

5 

5 

5 

7 

8 

3 

128  MULTIPLICATION  AND  DIVISION 

ORAL  EXERCISE 

1.  How  many  6's  are  there  in  6  ?  in  12  ?  in  18  ?  in  42  ? 

2.  State  rapidly  the  results : 

54-^6  30-6  48-^6  36-^6 

3.  Read  and  learn  this  table : 


4. 


12  ^  6  =  2             30  -^ 

-6  = 

=  5 

48^ 

^6=    8 

18^6  =  3             36  H 

-6  = 

=  6 

54^ 

^6=    9 

24  ^  6  =  4              42  ^ 

-6  = 

=  7 

60  H 

f-6  =  10 

State  rapidly  the  results  : 

6x6               7x6 

54- 

6 

3x6 

6x5               6x7 

54- 

•9 

18-6 

30-6             42-6 

48- 

6 

6x6 

30-5             42-7 

8x 

6 

36-6 

WRITTEN  EXERCISE 

1.  At  6^  a  pound,  how  many  pounds  of  sugar  can  you 
buy  for  48(^?   for  54(^?   for  60(^? 

2.  At  6^  a  box,  how  many  boxes  of  crackers  can  you  buy 
for  54(ji?   for  36(^?   for  42(^? 

3.  At  6^  a  yard,  how  many  yards  of  cloth  can  you  buy 
for  24(^?   for  30(^?   for  66^? 

4.  If  the  pupils  of  a  class  of  30  march  in  rows  of  6,  how 
many  rows  are  there  ? 

5.  Copy  and  complete : 

36 -=6  -6  =  3  30-6  = 


DIVISION 


129 


Further  Work  in  Division.  We  have  already  learned 
how  to  divide  by  a  number  of  one  figure,  and  we  shall 
now  consider  the  reasons  more  fully.  For  example,  to 
divide  628  by  2  we  write  the  numbers  as 
here  shown. 

We  see  that  6  hundreds  ^2  =  3  hundreds, 
and  we  write  the  3  in  the  hundreds'  place, 
below  the  dividend. 

Then  2  tens  -^-  2  =  1  ten,  and  we  write  the  1  in  the  tens' 
place,  below  the  dividend. 

Then  8  ones  -^2  =  4  ones,  and  we  write  the  4  in  the  ones' 
place,  below  the  dividend. 

The  quotient  is  314. 


WRITTEN  EXERCISE 


Divide  the  following : 


1.  648- 

-2. 

9.  846^2. 

17.  468- 

-2. 

2.  639- 

-3. 

10.  693-5-3. 

18.  936- 

-3. 

3.  444- 

-4. 

11.  448-^4. 

19.  840- 

-4. 

4.  884- 

-4. 

12.  848^4. 

20.  888- 

-8. 

5.  556- 

-5. 

13.  550-5. 

21.  505- 

-5. 

6.  666- 

-6. 

14.  660-6. 

22.  868- 

-2. 

7.  600- 

-6. 

15.  500-5. 

23.  777- 

-7. 

8.  448- 

-2. 

16.  336  H- 3. 

24.  999- 

-9. 

25.  A  ma 
many  lamb 

26.  A  dej 

many  coats 

in  paid  $360  for  some  lambs  at  $3  each.    I 
3  did  he  buy  ? 

der  paid  $408  for  some  coats  at  $4  each.  I: 
did  he  buy  ? 

^ow 
ow 

130 


MULTIPLICATION  AND  DIVISION 


ORAL  EXERCISE 

1.  Add  the  columns  of  7's,  from  one  7  to  five  7's. 

2.  On  the  blackboard  and  on  paper  build  more  columns 
of  7's,  until  you  have  ten  7's  in  the 

last  column.    How  many  columns  are 
there  ? 

3.  Read  the  columns,  thus :  "  One 
7  is  7,  two  7's  are  14,"  and  so  on. 

4.  How  many  are  five  7's  ?  six  7's  ? 
seven  7's  ?  eight  7's  ?  nine  7's  ?  ten  7's  ? 

5.  Read  and  learn  this  table  of  7's  : 
2x7  =  14  5x7=35  8x7=56 
3x7=21  6x7=42  9x7=63 
4x7=28               7x7=49              10x7=70 

6.  How  much  is  1x7?  7x1?  7x0?  0x7? 

7.  How  much  is  7  +  7  +  7  +  7  +  7  +  7?  What  short  way 
is  there  of  finding  the  answer  ? 

8.  State  rapidly  the  following  products : 

3x7      7x6      7x9  7x5 

7x3       9x7      7x0  0x7 

4x7      7x7      7x2  2x7 

7x4       7x8       7x1  5x7 

9.  What  is  the  cost  of  6  tables  at  $7  each  ? 

10.  What  is  the  cost  of  7  desks  at  |3  each,  and  a 
teacher's  desk  at  $7? 

11.  What  is  the  cost  of  9  yd.  of  cahco  at  7^  a  yard  ?  of 
2  yd.  of  trimming  at  7^  a  yard  ? 


TABLE  OF  SEVENS  131 

ORAL  EXERCISE 

1.  Recite  the  table  of  7's  from  1  x  7  to  10  x  7. 

2.  At  7^  a  yard,  what  will  8  yd.  of  ribbon  cost? 

3.  At  7^  a  pound,  what  will  9  lb.  of  sugar  cost? 

State  these  products : 

4.  4  X  7.  8.  8  X  7.  12.  6x7.  16.  2  x  7. 

5.  9  X  7.  9.  7  X  7.  13.  7  x  1.  17.  1x7. 

6.  7x3.  10.  3x7.  14.  5  X  7.  18.  0x7. 

7.  7x2.  11.  7x5.  15.  10  x  7.  19.  7x4. 

State  the  answers : 

20.  6  X  7  +  4.  23.  2  X  7  +  1.  26.  8  x  7  +  5. 

21.  6  X  7  +  6.  24.  9  X  7  +  5.  27.  9  x  7  +  2. 

22.  4  X  7  +  3.  25.  5  X  7  +  2.  28.  7  x  7  +  3. 


WRITTEN  EXERCISE 

Multiply  the  following : 

1.                 2.                 3.  4. 

101             102             112  132 

7                7                7  7 


5. 

6. 

335 

227 

7 

7 

7. 

8. 

9. 

10. 

11. 

12. 

200 

204 

224 

324 

368 

362 

7 

7 

7 

7 

7 

7 

13. 

14. 

15. 

16. 

17. 

18. 

400 

409 

419 

439 

489 

777 

7 

7 

7 

7 

7 

9 

132  MULTIPLICATION  AND  DIVISION 

ORAL  EXERCISE 

1.  How  many  7's  are  there  in  7  +  7  4-  7  ?  in  21  ? 

2.  How  many  7's  are  there  in  28  ?  in  35  ?  in  42  ? 

3.  State  rapidly  the  results : 

70-^7  63H-7  14^7  49^7 

4.  Read  and  learn  this  table : 


14^7  = 

=  2 

35- 

^7  = 

=  5 

56-4-7=    8 

21-^7  = 

=  3 

42- 

h7  = 

:6 

63-4-7=    9 

28^7  = 

=  4 

49- 

^7  = 

=  7 

70-^7  =  10 

5.  State  rapidly 

the  results : 

8x7 

9x7 

6x 

7 

5x7 

7x8 

7x9 

7x 

6 

7x5 

66-^7 

63^7 

42-^ 

7 

35^7 

66^8 

63^9 

42-4- 

6 

35^5 

WRITTEN  EXERCISE 

1.  There  are  56  children  marching  in  rows  of  7.    How 
many  rows  are  there  ? 

2.  An  open  trolley  car  with  7  cross  seats  will  seat  35 
persons.   How  many  persons  can  sit  on  each  seat  ? 

3.  Mary  spent  42^  for  6  yards  of  calico.   How  much  did 
she  pay  a  yard  ? 

4.  Kate  spent  63^  for  7  yards  of  ribbon.    How  much  did 
she  pay  a  yard  ? 

5.  A  dealer  paid  |42  for  7  tables.   How  much  did  he  pay 
for  each  table  ? 


DIVISION"  133 

Division  Continued.  A  farmer  bought  7  cows  for  $441. 
What  was  the  average  price  per  cow? 

We  see  that  each  cow  cost  $441  -^  7. 

We  see  that  7  is  not  contained  in  4,  so  we 
take  44  and  divide  it  by  7. 

We  know  that  6x7=  42,  and  so  we  see 
that  44  -^  7  =  6,  with  a  remainder  of  2.    Since  we  have 
divided  44  tens,  we  write  the  6  in  the  tens'  place. 

The  remainder,  2,  is  tens ;  so  2  tens  + 1  =  21,  and 
21^7=3.    We  write  the  3  in  the  ones'  place. 

The  quotient  is  63,  and  so  the  average  price  was  $63. 

Check.    7  X  63  =  441,  the  dividend. 

The  teacher  may  ask  the  pupils  to  label  the  numbers  in  division,  that  is, 
to  place  the  dollar  sign  before  441  and  63  ;  but  the  business  man  would  not 
do  this  in  such  a  case.  The  fact  that  |6  -^  $2  =  3  and  $6  -r-  2  =  $3  makes 
the  use  of  labels  in  division  very  difficult  for  children  as  early  as  this. 

It  should  be  noticed  that  division  by  8  and  division  by  9  are  allowable  on 
this  page,  provided  the  other  factor  in  each  separate  division  is  7  or  less. 

WRITTEN  EXERCISE 

1.  At  $7  each,  how  many  calves  can  a  farmer  buy  with 
$364?  with  $371?   with  $378?  with  $714? 

2.  If  there  are  147  Boy  Scouts  marching  in  7  equal 
squads,  how  many  are  there  in  each  squad  ? 

Divide  the  following,  and  check: 

3.  651 H- 7.  7.726-6.  11.725-5. 

4.  654-2.  8.  567-7.  12.  511-7. 
5.648-4.  9.679-7.  13.456-8. 
6.  635  -  5.                10.  434  -  7.  14.  909  -  9. 


134 


MULTIPLICATION"  AND  DIVISION 


8  X  8  =  64 

9  X  8  =  72 
10  X  8  =  80 


ORAL  EXERCISE 

1.  Add  the  columns  of  8's  from  one  8  to  five  8's. 

2.  Build  more  columns  of  8's,  until  you  have  ten  8's 
in   the  last  column.    Then   read   the 
columns,  thus :  "  One  8  is  8,  two  8's 
are  16,"  and  so  on. 

3.  How  many  are  five  8's?  six 
8's?  seven  8's?  eight  8's?  nine  8's? 
ten  8's? 

4.  Read  and  learn  this  table  of  8's : 

2x8  =  16  5x8  =  40 

3x8  =  24  6x8  =  48 

4x8  =  32  7x8  =  56 

5.  How  much  is  1x8?   8x1?   8x0?   0x8? 

6.  How  much  is  8  +  8  +  8  +  8  +  8?   What  is  the  short 
way  of  finding  the  answer  ? 

7.  State  rapidly  the  following  products : 
6x8  8x2  7x8 
8x5               3x8  8x6 
4x8               8x0               2x8 
8x4               8x3               8x8 

8.  At  8^  each,  how  much  will  7  melons  cost? 

9.  At  $8  each,  how  much  will  9  tables  cost  ? 

10.  At  8^  each,  how  much  will  8  notebooks  cost? 

11.  At  8  miles  an  hour,  how  far  will  a  man  drive  a 
team  of  horses  in  2  hours? 

12.  At  8^  each,  how  much  will  6  grapefruits  cost? 


8x9 
6x8 
8x7 
8x1 


TABLE  OF  EIGHTS  135 

ORAL  EXERCISE 

1.  Recite  the  table  of  8's  from  1  x  8  to  10  x  8. 

2.  Recite  the  table  of  8's  from  8xlto8xl0. 

State  the  products : 

3.  3  X  8.         7.  8  X  3.  11.  8x9.  15.  2  x  8. 

4.  7  X  8.         8.  5  X  8.  12.  8x2.  16.  10  x  8. 

5.  9  X  8.         9.  6  X  8.  13.  1x8.  17.  8  x  6. 

6.  8x5.        10.  8x0.  14.  0  X  8.  18.  4x8. 

State  the  answers : 

19.  5  X  8  +  4.  21.  8  X  7  +  6.  23.  6  x  8  +  2. 

20.  4  X  8  +  3.  22.  2  X  8  +  1.  24.  8  x  2  +  1. 

WRITTEN  EXERCISE 


Multiply  the  following : 

1. 

2. 

3. 

4. 

5. 

6. 

200 

201 

202 

212 

242 

346 

8 

8 

8 

8 

8 

8 

7. 

8. 

9. 

10. 

11. 

12. 

300 

360 

361 

365 

378 

888 

8 

8 

8 

8 

8 

3 

13. 

14. 

15. 

16. 

17. 

18. 

400 

470 

475 

486 

498 

678 

8 

8 

8 

8 

8 

4 

19. 

20. 

21. 

22. 

23. 

24. 

675 

582 

625 

675 

687 

508 

8 

8 

8 

8 

8 

9 

136  MULTIPLICATION  AND  DIVISION 

ORAL  EXERCISE 

1.  How  many  8's  are  there  in  16  ?  in  24  ?  in  40  ? 

2.  State  rapidly  the  results : 

32^8  40-8  24^8  80-8 

3.  Read  and  learn  this  table : 


-8  =  2 

40  -  8  =  5 

64-8=    8 

-8  =  3 

48  -  8  =  6 

72-8=    9 

-8  =  4 

56  -  8  =  7 

"  80-8  =  10 

4.  How  many  8's  are  there  in  32  ?  in  48  ?  in  72  ? 

WRITTEN  EXERCISE 

1.  At  $8  each,  how  many  rocking-chairs  can  be  bought 

for  $72  ?  for  $80  ?  for  $66  ? 

2.  At  8^  a  quart,  how  many  quarts  of  strawberries  can 
be  bought  for  64(^  ?  for  72(^  ? 

3.  A  class  has  been  weaving  mats  like 
this.  How  many  horizontal  strips  are  there  ? 
How  many  vertical  ones  ?  How  many  in  all  ? 

4.  In  the  picture  you  see  8  meshes  on 

each  hne.    How  many  meshes  are  there  on  2  lines  ?   How 
many  are  there  on  3  Hnes  ?  How  many  are  there  on  4  hnes  ? 

Divide  the  following : 

5.64-5-8.        7.888-8.      9.480-8.      11.560-8. 
6.  640  -  8.      8.  880  h-  8.    10.  568  -  8.     12.  808  -  8. 


TABLE  OF  NmES 


137 


9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

ORAL  EXERCISE 

1.  State  the  sum  of  each  of  these 
columns  of  9's  thus :  9,  18,  and  so  on. 

2.  Count  by  9's  from  9  to  90. 

3.  How  many  9's  do  you  see  in  the 
column  that  makes  36  ?  in  the  one  that 
makes  45  ? 

4.  Read  and  learn  this  table  of  9's : 

2x9  =  18  5x9  =  45  8x9  =  72 

8x9  =  27  6x9  =  54  9x9  =  81 

4x9  =  36  7x9  =  63    .         10x9  =  90 

5.  How  much  is  1x9?  9x1?  9x0?  0x9? 

6.  State  rapidly  the  following  products : 

9x3  9x5  9x7  9x1 
9x6  9x0  8x9  7x9 
9x2      9x8       9x9       9x4 


WRITTEN  EXERCISE 

1.  Write  ten  columns  of  9's,  as  in  Ex.  1  above,  from 
one  9  to  ten  9's.    Add  each  column. 

2.  A  man  earns  $10  a  week.    How  much  does  he  earn 
in  7  weeks  ?  in  9  weeks  ?  in  6  weeks  ? 

3.  John's  father  sold  9  tables  at  $8  apiece.   How  much 
did  he  receive  for  all  the  tables  ? 

4.  If  you  buy  9  oranges  at  5^  each,  and  9  bananas  at 
3^  each,  how  much  do  you  pay  for  all? 


138  MULTIPLICATION  AKD  DIVISION 

ORAL  EXERCISE 

1.  At  9^  each,  what  will  9  pencils  cost? 

2.  At  9  ^  a  gallon,  what  will  7  gallons  of  oil  cost  ? 

3.  At  9  ^  a  quart,  what  will  6  qt.  of  strawberries  cost  ? 

4.  At  9  children  to  a  group,  how  many  children  in 
8  groups?  in  6  groups?  in  5  groups? 

5.  At  9^  each,  how  much  must  a  newsdealer  pay  for 
8  magazines? 

State  the  answers : 

6.  2  X  9  +  1.  9.  8  X  9  +  7.  12.  6  x  9  +  4. 

7.  4  X  9  +  2.  10.  9  X  7  +  6.  13.  9  x  6  +  7. 

8.  7  X  9  +  4.  11.  9  X  3  +  8.  14.  6  x  9  +  3. 

WRITTEN  EXERCISE 

Multiply  the  following : 


1. 

2. 

3. 

4. 

5. 

6. 

243 

320 

406 

572 

863 

742 

9 

9 

9 

9 

9 

9 

7. 

8. 

9. 

10. 

11. 

12. 

982 

989 

909 

879 

859 

576 

3 

5 

9 

6 

5 

8 

13. 

14. 

15. 

16. 

17. 

18. 

456 

686 

489 

539 

839 

983 

9 

9 

5 

6 

7 

9 

19.  A  man  bought  some  sugar  for  20^,  and  3  packages 
of  oatmeal  at  9  ^  each.   How  much  did  he  pay  for  all  ? 


TABLE  OF  NINES 


139 


ORAL  EXERCISE 

1.  Recite  the  table  of  9's  from  1  x  9  to  10  x  9. 

2.  Recite  the  table  of  9's  from  9  x  1  to  9  x  10. 


State  these  products : 
3.  6  X  9.  8.  4  X  9. 


4.  5x9. 

5.  8  X  9. 

6.  9x6. 

7.  9x5. 


9.  2x9. 

10.  3x9. 

11.  9x4. 

12.  9x7. 


13.  7x9. 

14.  0x9. 

15.  9  X  10. 

16.  9x1. 

17.  9x8. 


State  the  answers 

23.  6x9  +  5. 

24.  7x9  +  3. 


25.  9x9  +  7. 

26.  5x9  +  3. 


18.  1x9. 

19.  9x9. 

20.  9x3. 

21.  9x2. 

22.  10  X  9. 

27.  7x9  +  2. 

28.  6x9  +  4. 


WRITTEN  EXERCISE 

Multiply  the  following: 


1. 

2. 

3. 

4. 

5. 

6. 

765 

802 

732 

678 

496 

687 

9 

9 

9 

9 

9 

9 

7.. 

8. 

9. 

10. 

11. 

12. 

268 

265 

295 

275 

587 

809 

9 

9 

9 

9 

9 

8 

13. 

14. 

15. 

16. 

17. 

18. 

399 

373 

387 

309 

398 

878 

9 

9 

9 

6 

7 

8 

EP 

140  MULTIPLICATION  AND  DIVISION 

ORAL  EXERCISE 

1.  How  many  9's  are  there  in  18  ?   in  27  ?   in  36  ? 

2.  At  $9  each,  how  many  coats  can  be  bought  for  $45  ? 
for  $54?   for  $63? 

3.  At  $9  each,  how  many  dresses  c^n  be  bought  for  $27  ? 
for  $18?   for  $36?   for  $72? 

4.  State  rapidly  the  results  : 

18-9  27-9  36-9  45-9 

5.  Read  and  learn  this  table : 

18-9  =  2  45-9  =  5  72-9=    8 

27-9  =  3  54-9  =  6  81 -9  =9 

36 -9  =  4  63 -9  =  7  90 -9  =  10 

WRITTEN  EXERCISE 

1.  How  many  baseball  teams,  each  made  up  of  9  boys, 
can  be  formed  from  27  boys  ? 

2.  How  many  baseball  teams,  each  made  up  of  9  boys, 
can  be  formed  from  36  boys  ? 

3.  In  this  school  there  are  54  boys,  and  the  boys  are 
divided  into  baseball  nines.    How  many  nines  are  there  ? 

Divide  the  folloiohig : 

4.  180  -  9.        8.  189  -  9.  12.  900  -  9. 
5.279-9.        9.540-9.  13.990-9. 

6.  369  -  9.       10.  360  -  9.  14.  999  -  9. 

7.  459  -  9.       11.  450  -  9.  15.  909  -  9. 


EEVIEW  141 

ORAL  EXERCISE 

Multiply  each  of  the  numbers  3, 6,  ^,  9,  7, 5, 8, 4,  in  turn : 

1.  By  4,  and  add  3  to  the  product. 

2.  By  5,  and  add  4  or  3  to  the  product. 

3.  By  6,  and  add  5,  4,  or  3  to  the  product. 

4.  By  7,  and  add  6,  5,  4,  or  3  to  the  product. 

5.  By  8,  and  add  7,  6,  5,  4,  or  3  to  the  product. 

6.  By  9,  and  add  8,  1,  6,  5,  4,  or  3  to  the  product. 

The  teacher  should  direct  the  number  to  be  added  each  time.  The 
numbers  to  be  multiplied  should  be  written  on  the  blackboard  and  the 
products  read  in  the  order  given. 

7.  If  you  are  sent  to  the  grocer's  for  7  lb.  of  sugar  at 
6^  a  pound,  and  2^  worth  of  candy,  how  much  money 
must  you  pay  the  grocer? 

8.  If  you  are  sent  to  buy  9  lb.  of  sugar  at  6^  a  pound, 
and  5^  worth  of  cloves,  how  much  must  you  pay? 

9.  Frank  has  to  buy  8  lb.  of  sugar  at  5^  a  pound,  and 
7^  worth  of  cinnamon.    How  much  must  he  pay  ? 

10.  John  is  keeping  store,  and  he  has  6  piles  of  apples, 
9  apples  in  each  pile,  and  4  apples  besides.  How  many 
apples  are  there  in  all? 

11.  Some  boy  scouts  are  divided  into  6  squads  of  8  boys 
each,  and  there  are  4  boys  over.  How  many  boys  are 
there  in  all  ? 

12.  In  one  class  there  are  4  rows  of  8  pupils  each,  and 
3  pupils  over.    How  many  pupils  are  there  in  aU  ? 


142  MULTIPLICATIOK  AND  DIVISION 

ORAL  EXERCISE 

1.  Count  by  lO's  from  one  10  to  ten  lO's. 

2.  How  many  are  three  lO's  ?  seven  lO's  ? 

3.  Recite,  "One  10  is  10,  two  lO's  are  20,"  and  so  on  to 
"tenlO'sarelOO." 

4.  Read  and  learn  the  table  of  lO's : 

2x10  =  20  5x10=50  8  x  10  =   80 

3x10  =  30  6x10=60  9x10=   90 

4x10  =  40  7x10=70         10x10  =  100 

5.  How  much  is  10  x  5?  10  x  7?  10  x  2?  10  x  9? 

6.  A  girl  bought  3  cans  of  soup  at  10(^  each,  and  a 
pound  of  figs  for  20^.    How  much  did  she  pay? 

7.  If  Mary  buys  4  melons  at  10^  each,  and  an  orange 
for  5^,  how  much  must  she  pay? 

WRITTEN  EXERCISE 

1.  Build  ten  columns  of  lO's,  from  one  10  to  ten  lO's. 
Add  each  column. 

2.  Write  the  multiplication  table  of  lO's  from  1  x  10, 
and  2  X  10  to  10  X  10. 

3.  Write  the  multiplication  table  of  lO's  another  way, 
from  10  X  1,  and  10  x  2  to  10  x  10. 

4.  Complete  and  learn  this  table : 

20-5-10=  50-5-10=  80-5-10  = 

30  +  10=  60-5-10=  90-5-10  = 

40-h10=  70  +  10=  100  +  10=- 


EEVIEW  ■  143 

ORAL  DRILL  IN  MULTIPLICATION 

Multiply  the  following  nmnbers  by  2  and  by  3 : 

1.  21       23        32       31       22       83       41       43       42 

Multiply  the  following  numbers  by  4  and  by  5 : 

2.  20       30        40        50        70        21        31        80        41 

Multiply  the  following  numbers  by  6  and  by  7 : 

3.  11       50       90        70        21        81        60       31        80 

4.  20       61        51        30        91        40       41        10        71 

Multiply  the  following  numbers  by  8  and  by  9 : 

5.  20       91       30       51       70       31       80       200       111 

6.  41       50       21       60       61       40       71       310       211 

WRITTEN  EXERCISE 

Multiply  the  following : 

1.                 2.                  3.  4.  5.  6. 

746     829     607  892  487  983 

3       6       9  6  8  7 


7. 

8. 

209 

516 

4 

7 

13. 

14. 

688 

992 

8 

4 

9. 

10. 

11. 

12. 

837 

676 

893 

477 

5 

9 

3 

6 

15. 

16. 

17. 

18. 

347 

^  456 

833 

646 

9 

8 

9 

8 

144  MULTIPLICATION  AND  DIVISION 

ORAL  DRILL  IN  DIVISION 

Divide  each  nwriber  hy  ^,  S,  4,  and  5,  in  tarn,  giving 
quotients  and  remainders,  taking  first  the  lines  IS,-  and  then 
the  columns  4-13 : 


4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

13. 

1. 

21 

39 

26 

50 

46 

56 

28 

44 

40 

30 

2. 

38 

34 

51 

31 

22 

45 

59 

55 

49 

35 

3. 

25 

48 

32 

47 

41 

57 

42 

60 

23 

43 

Divide,  as  above,  each  number  by  6,  7,  8,  and  9,  in  turn, 
giving  quotients  and  remainders : 


17. 

18. 

19. 

20. 

21. 

22. 

23. 

24. 

25. 

26. 

14. 

10 

16 

19 

17 

20 

18 

21 

24 

23 

22 

15. 

13 

51 

44 

50 

31 

41 

57 

48 

52 

40 

16. 

15 

42 

29 

59 

26 

65 

47 

32 

64 

61 

WRITTEN  EXERCISE 

Divide  each  number  by  2,  3,  ^,  5,  6,  7,  8,  and  9,  in  turn, 
giving  quotients  and  remainders : 

1.  125  243  627  481  936  829 

2.  352  301  278  270  633  639 

3.  473  486  907  842  568  781 

4.  597  700  741  488  777  666 

Teachers  should  clearly  understand  that  drill  pages  of  this  kind  are 
to  be  used  only  until  the  pupil  has  attained  sufficient  proficiency  in  the 
processes.  The  drill  should  then  be  discontinued  and  new  work  should  be 
taken  up. 


USING  WHAT  YOU  HAVE  LEARNED  145 

V.   USING  WHAT  YOU  HAVE  LEAENED 
HOW  THE  CITY  BOY  AND  GIRL  USE  THEIR  ARITHMETIC 

1.  Mollie  pays  10^  a  day  for  trolley  fares  in  going  to 
school.  How  much  does  she  pay  each  week,  if  she  goes 
every  school  day?  How  much  does  she  pay  in  2  weeks? 

2.  Rob's  father  took  Rob  and  six  of  his  friends  to  see 
the  moving  pictures.  How  many  tickets  did  he  buy  in  all  ? 
How  much  did  it  cost  at  10  ^  each  ? 

3.  Tom's  father  sent  Tom  to  the  post  office  to  buy  25 
two-cent  stamps.   How  much  did  Tom  pay  for  the  stamps  ? 


4.  Some  children  in  a  city  school  made  these  baskets 
out  of  raffia.  The  raffia  for  the  three  baskets  cost  12^, 
and  each  took  the  same  amount.  What  was  the  cost  for 
each  basket?  What  would  be  the  cost  for  15  baskets? 

5.  If  each  basket  was  sold  for  10^,  what  was  the  gain  on 
each?  What  was  the  gain  on  the  three?  What  would  be 
the  gain  on  15  baskets  ? 

6.  Of  these  baskets  the  largest  holds  8  pt.  and  the 
smallest  holds  2  pt.  The  third  holds  half  as  much  as  the 
other  two  together.   How  much  does  the  third  hold  ? 

\ 


146  USING  WHAT  YOU  HAVE  LEARNED 

EARNING  AND  SPENDING 

1.  George  is  a  newsboy.  He  pays  3^  for  5  papers. 
How  much  does  he  pay  for  10  papers  ?  for  15  papers  ? 

2.  Harold  gets  25^  for  mowing  a  lawn.  If  he  mows  it 
4  times  a  month,  how  much  does  he  get  in  a  month  ? 

3.  If  it  costs  each  pupil  60^  a  year  for  schoolbooks, 
how  much  will  it  cost  3  pupils  each  year  ? 

4.  Anna  spends  5^  every  week  going  to  the  moving 
pictures.  There  being  52  weeks  in  a  year,  how  much 
would  she  save  in  a  year  if  she  did  not  go  ? 

5.  John  is  in  the  third  grade.  His  father  buys  him  a 
reader  for  40^,  an  arithmetic  for  30^,  a  spelling  book  for 
25^,  and  a  language  book  for  35^.  How  much  does  he 
pay  for  all  four  books? 

6.  In  Ex.  5,  if  John's  father  pays  for  the  books  with  a 
$2  bill,  how  much  change  should  he  receive  ? 

7.  If  you  earn  50^,  60^,  20^,  and  70^,  how  many  cents 
do  you  earn  in  all  ?   How  many  dollars  is  this  ? 

8.  Frank  earns  70^  and  50^.  How  many  cents  does  he 
earn  ?   Write  the  answer  also  as  dollars  and  cents. 

9.  Harold  sold  140  copies  of  the  Saturday  Evening  Post 
at  5^  each.  How  many  cents  did  he  receive?  How  many 
dollars  is  this  ? 

Instead  of  multiplying  5  by  140,  multiply  140  by  5. 

10.  Fred's  father  sent  him  to  the  post  office  for  125 
two-cent  stamps.  How  much  did  Fred  have  to  pay  for 
the  stamps? 


FEACTIONS  14T 

VI.  FRACTIONS 
ORAL  EXERCISE 

1.  Miriam  is  making  some  doll's  clothes  for  her  little 
sister's  doll.  She  has  a  piece  of  ribbon  16  in.  long  and  uses 
J  of  it.    How  many  inches  of  ribbon  does  she  use  ?   / 

2.  If  Miriam  had  used  J  of  the  16  in.  of  ribbon,  how 
many  inches  of  ribbon  would  she  have  used  ? 

3.  If  Miriam  had  used  J  of  the  16  in.  of  ribbon,  how 
many  inches  of  ribbon  would  she  have  used  ? 

4.  How  do  you  find  J  of  a  number?  How  do  you  find 
1^  of  a  number? 

5.  Miriam's  mother  has  24  yd.  of  calico,  and  she  tells 
Miriam  that  she  can  have  ^  of  it.  How  many  yards  does 
she  let  Miriam  have  ? 

6.  Can  you  tell  me  how  many  yards  Miriam's  mother 
had  left  after  she  gave  Miriam  ^  of  the  24  yd.?  How  do 
you  find  this? 

7.  How  do  you  find  |^  of  a  number?  After  you  have 
found  |-  of  a  number,  how  can  you  find  |^  of  the  number  ? 
■|  of  the  number  ?   •§•  of  the  number  ? 

8.  How  do  you  find  J  of  a  number  ?  After  this  has  been 
found,  how  can  you  find  |-  of  the  number  ?  How  can  you 
then  find  1|^  times  the  number  ? 

The  pupil  is  now  beginning  the  study  of  harder  fractions,  and  he  should 
be  led  to  see  the  need  for  the  work.  It  is  not  necessary  that  he  should  be 
able  to  answer  all  of  these  questions;  indeed,  it  is  better  that  he  should 
not  answer  them  too  readily,  if  at  all.  The  important  thing  is  to  let  the 
pupil  see  the  necessity  of  further  work  in  fractions. 


148 


FRACTIONS 


ORAL  EXERCISE 

1.  Tell  the  number  of  halves  in : 


1* 


2* 


H 


2.  Tell  the  number  of  feet  equal  to : 


J  ft. 


I  ft. 


fft. 


fft. 


3.  Tell  the  number  of  thirds  in 


1* 


1^ 


^3 


fft. 


SI 
^3 


10 


J  ft. 


42 
^3 


4.  Tell  the  number  of  fourths  in 


5.  Which  circles  show  you  that  3-  =  |^  +  J-  ? 

6.  How  many  sixths  do  you  see  in  J  of  the  circle  ? 

7.  In  the  whole  circle  how  many  sixths  do  you  see  ? 


WRITTEN  EXERCISE 


Divide  a  circle  into  halves,  fourths,  and  eighths,  and 


show  that  J  =  f  =  f  • 


2.  Draw  oblongs  4  inches  long  and  1  inch  wide.    Shade 
them  to  show  that  1  —  J  =  fj  l~f  =  4>  ^^^  i  +  i ~  2 • 

3.  If  a  man  has  $1840  and  spends  J  of  it,  how  much 
does  he  spend  ?   How  much  has  he  left  ? 


MEASURES 


149 


VII.   MEASURES 
ORAL  EXERCISE 

1.  Name  something  that  is  sold  by  the  bushel. 

2.  Name  some  kind  of  fruit  that  is  sold  by  the  peck. 

3.  How  many  pecks 
in  a  bushel  ? 

4.  How  many  quarts 
in  a  peck  ? 

5.  In  the  picture, 
point  to  the  liquid  pint, 
quart,  and  the  measure 
called  a  gallon  (gal.), 
which  holds  4  qt. 

6.  Point  to  the  dry 
quart,  peck,  and  bushel. 


Dry  Measure.    The  table  of  dry  measure  is  as  follows  : 

2  pints  (pt.)  =  1  quart  (qt.) 

8  quarts  =  1  peck  (pk.) 

4  pecks  =  1  bushel  (bu.) 

WRITTEN   EXERCISE 

1.  If  a  boy  feeds  his  pony  2  qt.  of  oats  three  times  a 
day,  how  many  quarts  will  he  feed  him  a  day  ? 

2.  How  many  quarts  in  2  pk.  ?   in  4  pk.  ?   in  1  bu.  ? 

3.  How  many  pecks  in  half  a  bushel  ?  in  10  bu.  ? 


160  MEASUKES 

ORAL  EXERaSE 

1.  If  you  put  a  pound  weight  on  one  side  of  the  scales, 
how  many  ounce  weights  must  be  put  on  the  other  side  to 
balance  it  ? 

2.  Then  how  many  ounces  make  a  pound  ?  Then  1  ounce 
is  what  part  of  a  pound  ? 


Weight.    The  table  of  weight  is  as  follows  : 
16  ounces  (oz.)  =  1  pound  (lb.) 

If  there  are  scales  in  the  school,  children  should  weigh  various  objects, 
and  also  find  that  16  ounces  =  1  pound.  Children  sometimes  make  bags 
of  different  sizes,  putting  in  enough  sand  to  make  them  weigh  1  lb.,  ^  lb., 
and  J  lb.  The  weights  are  then  told,  the  children's  eyes  being  closed. 


3.  The  average  height  and  weight  of  children  of  your 
age  is  about  as  follows : 


Boys 

Girls 

Boys                 Girls 

7yr. 

44  in. 

44  in. 

48  lb.         47  lb. 

Syr. 

46  in. 

46  in. 

52  lb.         50  lb. 

9yr. 

50  in. 

49  in. 

57  lb.          55  lb. 

Compare 

your  height 

and  wei 

ght  with  the  average. 

WRITTEN  EXERCISE 

1.  579  lb.  +  927  lb.  5.  981  lb.  -  264  lb. 

2.  648  lb.  +  879  lb.  6.  923  lb.  -  478  lb. 

3.  737  lb.  +  578  lb.  7.  961  lb.  -  389  lb. 

4.  998  lb.  +  287  lb.  8.  800  lb.  -  126  lb. 


SQUAKE  MEASURE 


151 


1  square  inch 
1  sq.  in. 


Area  of  a  Square  or  Oblong.    A  square  that  is  1  in.  on 
a  side  is  1  inch  square.  The  area  of  such 
a  square  is  1  square  inch. 

A  square  that  is  1ft.  on  a  side  is 
1  foot  square,  and  the  area  of  such  a 
square  is  1  square  foot. 

If  an  oblong  is  4  ft.  long  and  2  ft. 
wide,  its  area  is  8  square  feet.  There 
are  2  rows,  with  4  square  feet  in  a  row ; 
that  is,  there  are  2x4  square  feet.  We 
say  that  such  an  oblong  is  2  ft.  by  4  ft. 


lln. 


The  square  inch  and  square  foot  should  be  drawn  on  the  blackboard,  and 
the  idea  of  area  should  be  made  clear  by  numerous  simple  illustrations  like 
the  one  given  above.  The  pupils  should  ascertain  the  number  of  square 
inches  in  a  square  foot,  and  the  number  of  square  feet  in  a  square  yard. 

Square  Measure.  In  square  measure  we  use  the  following 
table : 

144  square  inches  (sq.  in.)  =  1  square  foot  (sq.  ft.) 
9  square  feet  =  1  square  yard  (sq.  yd.) 


WRITTEN  EXERCISE 

1.  Draw  a  square  yard,  representing  1  yd.  by  1  in.    This 
is  called  drawing  it  to  the  scale  of  1  in.  to  1  yd. 

2.  Draw  a  square  foot  to  the  scale  of  3  in.  to  1  ft. 

3.  If  an  oblong  is  3  in.  long  and  2  in.  wide,  how  many 
square  inches  has  it  ?   Draw  the  figure. 

4.  If  a  schoolroom  is  10  yd.  long  and  7  yd.  wide,  how 
many  square  yards  are  there  in  the  floor? 


152  MEASUEES 

ORAL  EXERCISE 

1.  The  top  of  a  box  is  an  oblong  3  in.  wide  and  6  in. 
long.    What  is  the  area? 

2.  A  sheet  of  paper  is  4  in.  by  7  in.    What  is  the  area  ? 

3.  A  pane  of  glass  is  9  in.  by  10  in.    What  is  the  area  ? 

4.  An  oblong  is  7  in.  long  and  3  in.  wide.  What  is  the 
area  ?  What  is  the  sum  of  all  the  sides  ? 

5.  A  square  is  4  yd.  on  a  side.  Find  the  area,  and  the 
sum  of  all  the  sides. 

The  teacher  may  introduce  the  word  "  perimeter,"  in  place  of  "  sum  of 
all  the  sides,"  if  desired.   Practice  should  be  given  in  estimating  areas. 

WRITTEN  EXERCISE 

1.  Draw  an  oblong  6  in.  long  and  4  in.  wide.  Find  the 
area  and  the  sum  of  all  the  sides. 

2.  Draw  an  oblong  one  half  as  long  and  one  half  as 
wide  as  the  first  oblong  (Ex.  1).    Find  the  area. 

3.  Find  the  area  and  the  sum  of  all  the  sides  of  an 
oblong  8  ft.  long  and  5  ft.  wide. 

4.  A  square  6  yd.  on  a  side  contains  how  many  square 
yards  ?   How  many  yards  in  the  sum  of  all  the  sides  ? 

5.  Measure  the  length  and  the  width  of  your  arithmetic. 
Each  page  contains  how  many  square  inches  ? 

6.  Draw  a  2-inch  square.  Draw  a  4-inch  square.  The 
2-inch  square  equals  what  part  of  the  4-inch  square? 
Find  the  area  and  the  sum  of  all  the  sides  of  the  2-inch 
square,  and  also  of  the  4-inch  square. 


REVIEW  153 

VIII.   REVIEW 
ORAL  EXERCISE 

1.  How  many  school  days  in  1  week  ?  in  2  weeks  ? 

2.  How  many  school  days  in  3  weeks  ?  in  5  weeks  ? 

3.  How  many  school  days  in  7  weeks  ?  in  8  weeks  ? 

4.  How  many  hours  are  you  in  school  in  the  forenoon  ? 
in  the  afternoon  ?  all  day  ? 

5.  How  many  hours  are  you  in  school  in  5  days  ? 


6. 

3  +  5.         11. 

5  +  3.         16. 

4  +  6. 

21. 

6  +  4. 

7. 

8-3.         12. 

8 

-  5.          17. 

10-4. 

22. 

10-6. 

8. 

3x5.         13. 

5 

X  3.         18. 

4x6. 

23. 

6x4. 

9. 

15  -H  3.       14. 

15  ^  5.       19. 

24  H- 4. 

24. 

24  H- 6. 

10. 

1  of  15.      15. 

1 

5 

of  15.      20. 

i  of  24. 

25. 

1  of  24. 

WRITTEN  EXERCISE 

Add  the  folloioing 

.* 

1. 

2. 

3. 

'  4. 

5. 

$2.78 

$4.87 

$17.29 

$26.48 

$34.75 

3.42 

6.93 

14.32 

42.76 

41.25 

4.20 

8.40 

.18 

39.37 

6.00 

6. 

7. 

8. 

9. 

10. 

$1.27 

$2.97 

$19.37 

$78.25 

$57.32 

2.43 

3.23 

23.48 

49.75 

49.68 

4.09 

5.71 

4.29 

33.33 

81.93 

.76 

8.49 

16.71 

49.67 

42.07 

5.34 

6.90 

18.35 

8.00 

61.00 

154  REVIEW 

ORAL  EXERCISE 

1.  If  Mary  finds  that  eggs  cost  40^  a  dozen,  how  much 
must  she  pay  for  2  dozen  eggs  ? 

2.  If  butter  costs  40^  a  pound,  how  much  must  Mary 
pay  for  2  lb.  of  butter  ? 

3.  If  oranges  cost  5  ^  apiece,  how  much  must  Mary  pay 
for  4  oranges  ? 

4.  If  cheese  costs  20^  a  pound,  how  much  must  Mary 
pay  for  3  lb.  of  cheese  ? 

5.  Mary  bought  2  cans  of  baking  powder  at  40^  a  can. 
How  much  did  she  pay  ? 

6.  4  +  7.         11.  7+4.         16.  5  +  8.         21.  8  +  5. 

7.  11-4.        12.  11-7.         17.  13-5.       22.  13-8. 

8.  4x7.         13.  7x4.  18.  5  X  8.         23.  8x5. 

9.  28  ^  4.       14.  28  -  7.        19.  40  ^  5.       24.  40  -  8. 
10.  1  of  28.      15.  1  of  28.      20.  1  of  40.      25.  i  of  40. 

WRITTEN  EXERCISE 

1.  How  much  must  Mary  pay  for  3  lb.  of  figs  at  18^ 
a  pound  ?   at  19  ^  a  pound  ? 

2.  How  much  must  Mary  pay  for  2  qt.  of  sirup  at  46^ 
a  quart  ?  at  48^  a  quart  ? 

3.  How  much  must  Mary  pay  for  3  tins  of  wafers  at 
27(^a  tin?   at  24(^a  tin? 

4.  How  much  must  Mary  pay  for  3  lb.  of  raisins  at  25^ 
a  pound  ?   at  23  ^  a  pound  ? 


EEVIEW 

155 

WRITTEN  EXERCISE 

Add  and  check  : 

1. 

2. 

3. 

4. 

5. 

$8.26 
9.42 

$4.79 
3.42 

$6.87 
4.91 

$81.96 

32.88 

$78.92 
81.36 

3.82 

5.39 

5.73 

56.42 

47.57 

1.23 

2.27 

1.06 

41.60 

37.43 

6. 

7. 

8. 

9. 

10. 

$9.83 
4.78 

$7.35 
8.42 

$7.34 
8.29 

$27.42 
19.37 

$21.97 
32.43 

6.42 

9.98 

6.42 

18.62 

68.74 

8.96 

.67 

4.31 

5.34 

42.96 

Subtract  and  check : 

11.      • 

12. 

13. 

14. 

15. 

$9.39 
6.43 

$8.72 
4.96 

$7.31 

2.48 

$15.78 
13.92 

$27.42 
16.96 

16. 

17. 

18. 

19. 

20. 

$8.21 
4.32 

$9.00 
4.76 

$8.10 
3.92 

$47.01 
22.43 

$68.75 
49.96 

21. 

22. 

23. 

24. 

25. 

$5.77 
2.68 

$9.11 
2.32 

$8.17 
4.96 

$37.82 
14.93 

$91.10 

28.75 

26. 

27. 

28. 

29. 

30. 

$9.07 
6.49 

$8.02 
3.70 

$6.00 
4.27 

$30.00 
6.94 

$90.04 
27.70 

)6                                         REVIEW 

WRITTEN  EXERCISE 

Multiply  the  following : 
1.                       2.                       3. 

271              $486              $595 
2                    3                    4 

4. 

$643 
5 

5. 

$781 
6 

6.         7.         8.         9.  10. 

$842      $937      $249      $342  $873 
7      8      9      7      8 

11.         12.         13.        14.  15. 

$998              $843              $777              $398  $873 
6              7              7              8  ■     .9 

16.  Divide  each  of  these  numbers  by  2  and  by  3  : 

276            378            612            342            486      '  570 

348            492            204            726            498  288 

222            528            180            414            336  960 

17.  Divide  each  of  these  numbers  by  4  and  by  5  : 

280            560            820            980            480  500 

460,           340             740             220             900  620 

18.  Divide  each  of  these  numbers  by  6  and  by  7 : 

420            840            462            210            294  378 

546            882            504            252            336  924 

19.  Divide  each  of  these  numbers  by  8  and  by  9  : 

720     360     288     504     648  936 

792     216     432     576     864  144 


REVIEW  167 

ORAL  EXERCISE 

Find  the  cost  of  the  following  : 

1.  2  doz.  eggs  at  40^  a  dozen ;  at  50^  a  dozen. 

2.  8  lb.  of  crackers  at  8^  a  pound ;  at  9^  a  pound. 

3.  2  lb.  of  tea  at  40^  a  pound ;  at  30  (^  a  pound. 

4.  5  lb.  of  prunes  at  7^  a  pound ;  at  8^  a  pound. 

5.  6  lb.  of  starch  at  9^  a  pound ;  at  10^  a  pound. 

6.  8  lb.  of  rice  at  8(^  a  pound ;  at  9(^  a  pound. 

7.  1  lb.  of  figs  at  20  (^  a  pound ;  at  22^  a  pound. 

8.  7  lb.  of  crackers  at  10^  a  pound ;  at  9^  a  pound. 

WRITTEN  EXERCISE 

Find  the  cost  of  the  following : 
1.  2  lb.  of  coffee  at  35^  a  pound ;  at  37^  a  pound. 
.  2.  4  lb.  of  raisins  at  12^  a  pound ;  at  14  (^  a  pound. 

3.  2  lb.  of  tea  at  48^  a  pound ;  at  46^  a  pound. 

4.  2  doz.  eggs  at  47^  a  dozen;  at  44^  a  dozen. 

5.  ^  doz.  oranges  at  60^  a  dozen;  at  80^  a  dozen. 

6.  1  doz.  bananas  at  36  (^  a  dozen ;  at  40^  a  dozen. 

7.  2  doz.  bananas  at  36^  a  dozen  ;  at  38^  a  dozen. 

Find  the  total  cost  in  each  example : 

8.  2  lb.  of  sugar  at  6^  a  pound;  3  lb.  of  prunes  at  8^ 
a  pound ;  5  lb.  of  rice  at  8^  a  pound. 

9.  3  lb.  of  starch  at  9^  a  pound ;  2  lb.  of  crackers  at  12^ 
a  pound ;  ^  doz.  oranges  at  40^  a  dozen. 


158  REVIEW 

WRITTEN  EXERCISE 

1.  Write  in  figures :  five  thousand  fifty-five ;  eighteen 
hundred  fifty-eight ;  seven  thousand  three  hundred  forty- 
six  ;  nineteen  hundred  fourteen. 

2.  The  rents  for  an  office  building  for  one  month  were 
as  follows :  first  floor,  $384 ;  second  floor,  |290 ;  third 
floor,  $275;  fourth  floor,  $186.  What  was  the  total  rent? 

3.  Four  coal  trains  left  the  mines  loaded  as  follows: 
the  first  had  1100  tons  of  coal;  the  second,  1275  tons; 
the  third,  998  tons;  the  fourth,  1822  tons.  How  many 
tons  of  coal  did  the  four  trains  carry? 

It  is  legitimate  to  use  the  word  "  ton  "  as  an  indefinite  term  at  the  pres- 
ent time.  Children  hear  such  words  used,  and  the  teacher  may  explain 
them  informally.   Similarly  for  such  words  as  "  mile  "  and  "  year." 

4.  A  merchant's  receipts  for  one  day  were  $298.85, 
$624.88,  and  $157.60.    What  were  the  total  receipts? 

5.  A  town  has  to-day  8967  inhabitants.  It  gained  128.9 
in  ten  years.   How  many  were  there  ten  years  ago  ? 

6.  A  train  started  with  500  passengers  and  made  four 
stops  on  a  trip.  At  the  first  stop  89  passengers  got  off ; 
at  the  second,  78 ;  at  the  third,  122 ;  at  the  fourth,  55. 
How  many  passengers  remained  on  the  train? 

7.  By  one  way  it  is  411  miles  from  New  York  to 
Buffalo  and  541  miles  from  Buffalo  to  Chicago.  How  far 
is  it  from  New  York  to  Chicago  ? 

8.  A  dealer  offered  $7.85  apiece  for  some  suits  of  clothes, 
but  $9.15  apiece  was  asked  for  them.  How  much  more 
was  asked  than  was  offered  for  the  suits? 


PEOBLEMS  159 

9.  A  farmer  paid  6^  a  pound  for  some  hogs.  He  kept 
them  a  week  at  no  expense,  dm*ing  which  time  they  gained 
58  lb.,  and  he  then  sold  them  for  6^  a  pound.  How  many 
cents  did  he  gain  by  keeping  them  ?   How  many  dollars  ? 

10.  If  it  costs  $129  to  run  a  locomotive  one  trip  between 
two  cities,  how  much  will  it  cost  for  nine  trips  ? 

11.  A  teacher  receives  $45  per  month  for  9  months. 
How  much  does  she  receive  in  all? 

12.  A  mile  contains  5280  ft.  How  many  feet  are  there 
in  half  a  mile  ? 

13.  If  milk  costs  7^  a  quart  and  a  family'  uses  2  qt.  a 
day,  how  much  will  be  the  milk  bill  for  7  da.  ? 

14.  A  man  paid  $487  for  some  land.  He  built  on  it  a 
house  costing  $2225  and  a  barn  costing  $250.  What  was 
the  total  cost  of  the  land  and  buildings  ? 

15.  Ralph  receives  $55  a  month  for  7  months,  and 
George  $45  a  month  for  9  months.  What  is  the  total 
amount  received  by  each? 

16.  What  is  the  cost  of  216  calves  at  $9  each? 

17.  A  farmer  paid  $329  for  7  cows.  How  much  did  he 
pay  for  each  cow  ? 

18.  What  is  the  cost  of  564  tons  of  coal  at  $6  per  ton? 

19.  What  is  the  cost  of  9  tables  fit  $17  each  ? 

20.  Frank  pays  a  debt  of  $26.17,  and  gives  in  payment 
3  ten-dollar  bills.    How  much  change  should  he  receive  ? 

21.  A  bushel  of  oats  weighs  32  lb.  How  many  pounds 
do  8  bu.  of  oats  weigh  ? 


160  REVIEW 

WRITTEN  EXERCISE 

Add  the  following ,  and  check: 


1. 

2. 

3. 

4. 

5. 

$5.43 

$9.34 

$8.27 

$11.17 

$13.37 

1.27 

2.18 

9.36 

25.25 

■  72.26 

3.19 

6.25 

10.19 

37.37 

87.19 

6. 

7. 

8. 

9. 

10. 

$2.03 

$8.12 

$12.12 

$14.05 

$30.03 

3.04 

7.32 

13.13 

11.10 

20.02 

3.21 

5.13 

21.21 

.  31.32 

40.01 

5.51 

6.41 

32.32 

23.50 

50.50 

6.18 

7.56 

18.72 

15.68 

19.87 

11. 

12. 

13. 

14. 

15. 

$4.06 

$5.17 

$13.78 

$16.27 

$15.76 

2.98 

6.24 

14.26 

18.42 

8.24 

3.74 

8.19 

19.16 

27.96 

24.16 

2.45 

3.32 

12.04 

11.34 

14.26 

6.17 

4.46 

18.75 

12.19 

18.91 

9.63 

8.75 

22.67 

19.84 

22.68 

16. 

17. 

18. 

19. 

20. 

$6.17 

$2.99 

$9.99 

$10.06 

4l.98 

2.98 

1.86 

1.06 

9.80 

10.47 

1.48 

3.47 

.   22.14 

4.29 

8.93 

3.65 

8.21 

13.87 

13.62 

26.12 

2.91 

•  1.69 

20.16 

8.75 

10.89 

1.64 

5.16 

7.98 

22.10 

37.16 

7.49 

8.22 

10.00 

41.09 

9.48 

DRILL  WORK 

161 

Subtract  the  folloioing, 

and  check : 

21. 

22. 

23. 

24. 

25. 

$7.45 
5.03 

$7.89^ 
4.63    , 

$8.59 
5.26 

$9.33 
7.29 

$36.55 
28.00 

26. 

27. 

28. 

29. 

30. 

$9.51 
3.28 

$5.65 
1.27 

$6.41 

2.38 

$6.73 
1.09 

$17.44 
8.36 

31. 

32. 

X 

33. 

^^3^' 

35. 

$8.63 
2.99 

$7.11 
4.09 

•  $9.16 
2.38 

$8.92 
3.19 

$24.31 
15.42 

36. 

37. 

38. 

39. 

40. 

$9.17 
6.29 

$8.45 
4.56 

$6.07 
3.08 

$9.36 
4.07 

$46.18 
20.09 

Multiply  the  following 

; 

41. 

42. 

43. 

44. 

45. 

$113 
3 

$224 
4 

47. 

$510 
5 

48. 

$1612 
6 

49. 

$1175 

8 

46. 

50. 

$950 

7 

$699 
5 

52. 

$907 
9 

53. 

$1128 

8 

$1750 

4 

51. 

54. 

55. 

$675 
8 

$709 

-    7 

$812 
9 

$1050 
9 

$1425 
6 

162  REVIEW 

56.  Divide  each  of  these  numbers  by  2  : 

468  456  372  331 

326  253  214  547 

57.  Divide  each  of  these  numbers  by  3  : 

354  365  624  484 

444  235  651  790 

58.  Divide  each  of  these  numbers  by  4 : 

924     824     955     564 
752     912     734     723 

59.  Divide  each  of  these  numbers  by  5  : 

510  520  644  770 

665  735  560  887 

60.  Divide  each  of  these  numbers  by  6  : 

666  636  732  727 
624            725             746            810 

61.  Divide  each  of  these  numbers  by  7 : 

728     785     812     861 
745     797     805  "   873 

62.  Divide  each  of  these  numbers  by  8  : 

728  656  592  392 

744  672  512  304 

63.  Divide  each  of  these  numbers  by  9  : 

333     738     549     567 
666     657     324     405 


634 

972 

418 

905 

408 

798 

891 

976 

592 

918 

961 

513 

590 

742 

623 

825 

822 

924 

845 

933 

910 

943 

935 

950 

928 

111 

984 

222 

702 

777 

801 

888 

DRILL  TESTS 


X63 


DRILL  TEST.     MULTIPLICATION 

Write  all  the  ansivers  in  two  minutes  or  less 


— 1. 

4x6. 

^dl. 

6x4. 

^21. 

7x5. 

31. 

9x6. 

---2. 

7x3. 

_^2. 

4x7. 

22. 

9x9. 

32. 

3x9. 

^3. 

8x2. 

13. 

8x6. 

^3. 

4x8. 

33. 

8x7. 

4. 

5x6. 

^14. 

7x4. 

24. 

6x5. 

34. 

4x9. 

-_    5. 

7x7. 

^15. 

5x7. 

_J25. 

7x9. 

35. 

9x8. 

6. 

6x3. 

16. 

8x3. 

^26. 

9x4. 

36. 

6x6. 

7. 

8x5. 

17. 

6x8. 

^27. 

5x8. 

37. 

8x8. 

^8. 

9x2. 

/18. 

3x8. 

28. 

9x7. 

38. 

5x9. 

-9. 

6x7. 

^19. 

7x8. 

29. 

8x4. 

39. 

7x6. 

10. 

9x5. 

20. 

9x3. 

^30. 

6x9. 

40. 

8x9. 

DRILL  TEST.     DIVISION 

Write  all  the  answers  in  two  minutes  or  less 


1.  12- 

-4. 

11. 

18- 

-6. 

21. 

64- 

-8. 

^1. 

35- 

-5. 

2.  12- 

-6. 

-^2. 

21- 

-7. 

22. 

45- 

-5. 

32. 

24- 

-4. 

3.  32- 

-8. 

13. 

24- 

-8. 

23. 

24- 

-6. 

33. 

72- 

-9. 

4.  54- 

-9. 

14. 

16- 

-4. 

24. 

28- 

-7. 

^34. 

27- 

-3. 

5.  36- 

-4. 

15. 

48- 

-8. 

25. 

63- 

-9. 

^5. 

42- 

-6. 

— 6.  63- 

-7. 

16. 

54- 

-6. 

26. 

27- 

-9. 

M. 

24- 

-2. 

-^.  48- 

-6.' 

17. 

72- 

-8. 

27. 

20- 

-4. 

^37. 

56- 

-7. 

^8.  45- 

-9. 

.AS. 

35- 

-7. 

28. 

56- 

-8. 

38. 

18- 

-9. 

^9.  28- 

-4. 

19. 

36- 

-9. 

29. 

36- 

-6. 

39. 

55- 

-5. 

--10.  49- 

-7. 

20. 

32- 

-4. 

30. 

42- 

-7. 

40. 

81- 

-9. 

164  USING  WHAT  YOU  HAVE  LEAENED 

IX.   USING  WHAT  YOU  HAVE  LEARNED 

A  BIRTHDAY  PARTY  *• 

1.  Louise  is  having  a  birthday  party.  She  bought  8 
small  candles  at  2^  each  and  one  larger  candle  for  3(^. 
How  much  did  she  pay  for  all  of  the  candles  ? 


2.  If  Louise  gave  the  storekeeper  25^  for  the  candles, 
how  much  change  did  she  get  back  ? 

3.  Seven  of  her  friends  came.  Ji  she  provided  four  pieces 
of  cake  for  each  one  who  came  and  four  for  herself,  how 
many  pieces  did  she  provide  ? 

4.  She  made  a  cake,  using  3  eggs  worth  36^  a  dozen, 
3^  worth  of  sugar,  2^  worth  of  flour,  and  2^  worth  of  other 
materials.   How  much  did  all  the  materials  cost  ? 


PROBLEMS  165 

BUYING  THINGS  WE  WOULD  LIKE 

1.  Frank  can  get  an  express  wagon  for  65  ^.  He  has  saved 
48^.    How  much  more  must  he  save  to  buy  the  wagon? 

2.  Fred  wants  a  bicycle.  He  sees  one  that  is  marked 
113.50.  The  dealer  tells  him  he  can  have  it  for  $1.25 
less.   How  much  will  the  bicycle  cost  him? 

3.  Kate  wants  a  tricycle.  Her  father  finds  that  one  will 
cost  $2.75.  If  he  gives  her  $5  for  her  birthday,  she  can 
buy  the  tricycle  and  then  have  how  much  money  left  ? 

4.  Louise  wants  a  pair  of  shears.  She  can  buy  them  for 
45^.  If  she  gives  the  dealer  a  dollar  bill,  how  much  change 
should  she  receive  ? 

5.  If  you  buy  a  box  of  water-color  paints  for  25^,  some 
brushes  for  18^,  some  colored  crayons  for  10^,  and  some 
paper  for  15^,  how  much  will  it  all  cost? 

6.  Louise  wants  to  weave  some  rugs  for  her  doll  house. 
She  finds  that  a  wooden  loom  will  cost  35^,  some  weaving 
needles  15^,  and  some  rug  yarn  35^.  How  much  will  it 
all  cost?  How  much  change  should  Louise  receive  if  she 
gives  the  dealer  a  dollar? 

7.  Kate  wants  a  fountain  pen.  She  can  buy  one  for  90^, 
but  by  paying  40^  more  she  can  buy  the  kind  she  wants. 
How  much  must  she  pay  for  the  pen  she  wants  ?  How  much 
change  should  she  receive  if  she  gives  the  dealer  $1.50  ? 

8.  Kate's  father  promised  her  a  hammock  and  a  swing 
for  her  birthday.  The  hammock  cost  $2.65  and  the  swing 
cost  $0.85.   How  much  did  the  two  cost  ? 


166  LITTLE  EXAMIKATIONS 

X.   LITTLE  EXAMINATIONS 

I.   1.  39  +  7.  5.  26  +  37.  9.  XX  =  (?). 

2.27  +  6.  6.63-41.  10.  $1.25  + 12.30. 

3.  28  +  9.  7.  9  X  6.  11.  4  x  6  +  2. 

4.  37  +  4.  8.  2  X  808.  12.  369  -^  9. 

II.   1.46  +  9.  5.72-36.  9.  XVII  =  (?).     ' 

2.  25  +  8.  6.  56  +  38.  10.  $2.36  +  $1.22. 

3.  79  +  2.  7.  8  X  9.  11.  7x8  +  6. 

4.  48  +  7.  8.  6  x  275.  12.  588  ^  7. 

III.  1.  37  +  7.  5.  52-29.  9.  XVI=(?). 

2.  38  +  8.  6.  94  +  23.  10.  $2.31  +  $1.92. 

3.  35  +  7.  7.  4  X  381.  11.  8x9  +  7. 

4.  76  +  8.  8.  6  X  384.  12.  576  -  6. 

IV.  1.  49  +  6.  5.  63-48.  9.  XIX  =  (?).   ' 

2.  56  +  7.  6.  7  X  8.  10.  $3.42  +  $1.73. 

3.  47  +  8.  7.  7  X  223.  11.  9x6  +  4. 

4.  58  +■  6.  8.  7  X  225.  12.  9  ft.  =  (?)  in. 

V.   1.  58  +  3.  5.  38  +  16.  9.  XIV  =  (?). 

2.  26  +  6.  6.  72  -  66.  10.  8  pt.  =  (?)  qt. 

3.  39  +  3.  7.  8  X  6.  11.  8  x  8  +  2. 

4.  67  +  9.  8.  9  X  288.  12.  512  -f-  8. 

These  Little  Examinations  may  be  used  on  different  days  near  the 
close  of  a  term.   Teachers  should  read  the  note  on  page  52. 


CHAPTER  IV 

I.  READING  AND  WRITING  NUMBERS 

ORAL  EXERCISE 

1.  Count  by  lO's  from  10  to  100. 

2.  Count  by  lOO's  from  100  to  1000. 

3.  Count  by  lOOO's  from  1000  to  10,000. 

4.  Count  by  10,000's  from  10,000  to  90,000. 


The  number  100,000  is  read  "  one  hundred  thousand." 
In  a  number  of  five  figures  a  comma   (,)  is  written 
between  the  thousands  and  the  himdreds.    In  23,546 

the  6  occupies  the  ones'  place, 
the  4  occupies  the  tens'  place, 
the  5  occupies  the  hundreds'  place, 
the  3  occupies  the  thousands'  place, 
the  2  occupies  the  ten-thousands'  place. 


Read  the  following : 

5.  40,000.         9.  41,000.  13.  41,500.  17.  41,525. 

6.  50,000.       10.  50,500.  14.  50,050.  18.  50,005. 

7.  60,000.       11.  63,000.  15.  63,075.  19.  63,975. 

8.  76,450.       12.  82,729.  16.  86,483.  20.  99,999. 

167 


168  BEADING  AND  WKITING  NUMBERS 

Roman  Notation.  The  Roman  notation,  used  chiefly  If  or 
numbering  the  chapters  of  books,  employs  seven  capital 
letters,  as  follows : 

Letters,       I      V       X       L         C         D  M 

Values,       1       5       10      50       100      500       1000 

The  first  nine  numbers  are  written  thus : 

I    II    III    IV  or  mi    V    VI    VII    VIII    IX       • 

The  tens  are  written  thus : 

X    XX    XXX    XL    L    LX    LXX    LXXX    XC 

The  hundreds  are  written  thus : 
C    CO    CCC    CD    D    DC    DCC    DCCC    DCCCC  or  CM 

The  numbers  from  eleven  to  nineteen  are  written  thus: 
XI    XII    XIII    XIV    XV    XVI    XVII    XVIII    XIX 

The  following  are  examples  of  other  numbers : 

XXIII  =  23  XCVIII  =  98  CLXVI  =  166 

XXXVI  =  36  LXXVI  =  76  CCCLIX  =  359 

MDCCCCXVII  or  MCMXVII  =  1917 

WRITTEN  EXERCISE 

Write  in  common  figures : 

1.  XI.  3.  XXVI.         5.  LXXII.         7.  LXXVII. 

2.  LXIV.         4.  LXVI.         6.  XCVII.         8.  XXXIV. 

Write  in  Roman  numerals : 
9.  31.         11.  42.         13.  67.         15.  175.  17.  1919. 

10.  89.         12.  91.         14.  75.         16.  150.  18.  1920. 


ADDITION 


169 


II.   ADDITION.  - 
WRITTEN  EXERCISE 

Copy,  add,  and  check  in  five  minutes  or  less 
1.  2.  3.  4. 


3 

45 

5 

28 

7 

33 

9 

48 

12 

35 

72 

82 

1 

56 

89 

6 

10 

1 

86 

4 

64 

21 

7 

17 

14 

65 

2 

17 

26 

4 

74 

51 

79 

94 

3 

25 

36 

10 

52 

8 

20 

Copy,  add,  and  check  in  six  minutes  or  less 
6.  7.  8.  9. 


10. 


10 

87 

3 

15 

20 

45 

16 

17 

13 

96 

1 

45 

12 

08 

12 

16 

28 

45 

8 

44 

2 

32 

13 

47 

13 

18 

13 

92 

19 

27 

19 

80 

10 

26 

24 

72 

11 

15 

21 

13 

17 

41 

80 

15 

65 

8 

78 

12 

68 

11.  A  farmer  sold  milk  on  four  days  as  follows  :  Monday, 
224  qt.;  Tuesday,  246  qt.;  Wednesday,  238  qt.;  Thursday, 
228  qt.   How  many  quarts  did  he  sell  in  all  ? 

12.  When  Ethel's  father  went  to  Chicago  he  paid  $12.80 
for  his  ticket,  $7.75  at  the  hotel,  $24.75  in  shopping,  and 
$875  for  an  automobile.    How  much  did  he  spend  in  all  ? 

13.  On  the  first  day  of  the  fair  7214  tickets  were  sold ; 
on  the  second  day  8112  tickets,  and  on  the  third  day  6125. 
tickets.    How  many  tickets  were  sold  on  the  three  days  ? 


170  SUBTRACTION 

III.    SUBTRACTION 
WRITTEN  EXERCISE 

1.  How  much  more  is  224  ft.  than  187  ft.  ? 

2.  How  many  less  are  224  men  than  301  men? 

3.  How  much  more  is  the  sum  of  426  and  182  than 
the  sum  of  97  and  58? 

4.  How  much  less  is  the  sum  of  196  and  259  than  the 
sum  of  437  and  296  ? 

5.  A  farmer  who  had  235  chickens  sold  86  of  them. 
How  many  had  he  left?  He  then  bought  52  more.  How 
many  chickens  did  he  then  have  ? 

6.  A  farmer  had  68  sheep.  After  buying  75  more,  how 
many  did  he  have  ?  If  he  then  sold  40  sheep,  how  many 
did  he  then  have  ? 

7.  A  man's  income  for  a  year  is  $1500  and  $280,  and 
his  expenses  are  $1275.   How  much  does  he  save  ? 

8.  A  man's  salary  is  $1400  a  year,  and  he  receives 
$180  from  a  house  which  he  rents.  His  expenses  for  the 
year  are  $1142.   How  much  does  he  save  ? 

9.  How  many  more  Boy  Scouts  are  there  in  a  regiment 
made  up  of  76  boys  under  twelve  years  of  age  and  89  boys 
over  twelve  years  of  age  than  there  are  in  a  regiment  of 
144  boys? 

10.  A  boy  had  a  kite  string  428  ft.  long.  He  tied  on 
856  ft.  more,  and  later  lost  68  ft.  in  a  tree.  How  many 
feet  of  string  did  he  have  left? 


DRILL  WORK  171 

ORAL  EXERCISE 

If  you  owe  the  following  sums,  how  much  change  should 
you  receive  from  $1  in  each  case? 

1.  90^     95(^     80^     85(^     70(^     l^     88(^     92(^     81^ 

2.  30(^     60(^     A.^     38(^     49(^     62(^     36(^     43(^     11^ 

3.  10(^     20^     25f    35(^     41(^     33(^     66(^     79(^     89(^ 

7/*  ?/0M  oi^e  ^Ae  folloioing  sums,  how  much  change  should 
you  receive  from  $2  in  each  case  ? 

4.  $1.25        $1.50        $1.75        $1.80        $1.90        $1.95 

5.  $1.35        $1.38        $1.62         $1.56        $1.88        $1.17 

6.  $1.82        $1.61        $0.75        $1.20        $1.32        $1.44 

If  you  owe  the  following  sums,  how  much  change  should 
you  receive  from  ^S  in  each  case  f 

7.  $2.25        $3.25        $4.75         $2.80        $3.50        $1.50 

8.  $3.80        $4.10        $2.60        $1.40        $2.10        $4.15 

9.  $2.78        $3.75        $4.60         $3.90        $2.01        $3.07 

WRITTEN  EXERCISE 

Subtrojct,  and  check  the  work : 

1.                    2.                    3.  4.  6. 

$281.42         $691.75         $298.30  $427.20  $532.60 

135.02          208.02           107.60  109.32  237.62 

6.  7.  8.  9.  10. 

$532.65    $281.92    $409.72    $672.35    $491.63 
206.39    192.60    286.58    148.39    269.75 


172  MULTIPLICATION 

IV.   MULTIPLICATION 

Terms  Used.  We  have  already  learned  that  when  we 
take  a  number  2  times  we  multiply  it  by  2,  that  when  we 
take  it  3  times  we  multiply  it  by  3,  and  so  on. 

Pupils  are  not  expected  to  learn  formal  definitions  at  this  stage. 

We  have  also  learned  (page  85)  the  names  of  the  terms 
used  in  multiplication.  These  are  multiplicand,  multiplier, 
and  p)roduct,  and  are  seen  in  the  next  example. 

Multiplying  Money.  If  a  bookseller  sells  7  books  at 
$1.25  each,  how  much  money  does  he  receive  for  them? 

We  see  that  we  must  multiply 
$1.25  by  7. 

We  first  see  that  7  x  5^  =  35(^, 
or  3  dimes  and  5  cents,  and  we 
write  the  5  in  the  cents'  place 
and  add  the  3  to  the  dimes. 

Then  7x2  dimes  =  14  dimes,  and  14  dimes  +  3  dimes  = 
17  dimes,  or  $1.70.  We  write  the  7  in  the  dimes'  place  and 
add  the  1  to  the  dollars. 

We  then  write  the  decimal  point,  to  separate  the  dollars 
from  the  dimes. 

Then  7  x  |1  =  $7,  and  $7  +  $1  =  $8,  and  we  write  the  8 
in  the  dollars'  place. 

The  product  is  $8.75,  and  so  the  bookseller  receives 
$8.75  for  the  7  books.  ' 

Therefore,  to  multiply  United  States  m,oney,  multiply  as 
with  other  numbers,  placing  the  decimal  point  in  the  product 
below  the  decimal  point  in  the  m,ultiplicand.  ___ 2_£_ 


$1.25  multiplicand 

7  multiplier 
$8.75  product  • 


DRILL  WOR 

K 

173 

WRITTEN  EXERCISE 

Multiply  the  following : 

1. 

2. 

3. 

4. 

5. 

135 

2 

$1.35 

2 

275 

2 

$12.75 
2 

$10.20 

4 

6. 

7. 

8. 

9. 

10. 

$3.75 
2 

$1.35 
3 

$7.25 
3 

$18.60 
4 

$20.30 
5 

11. 

12. 

13. 

14. 

15. 

$9.30 
4 

$8.95 
4 

$2.33 
5 

$23.42 
5 

$24.70 
6 

16. 

17. 

18. 

19. 

20. 

$4.«1 
6 

$4.09 
6 

$7.28 
6 

$43.00 

7 

$36.75 
5 

21. 

22. 

23. 

24. 

25. 

$3.09 
7 

$3.59 
7 

$4.86 
8 

.      $71.93 
8 

$49.78 
6 

26. 

27. 

28. 

29. 

30. 

$6.32 
9 

$2.13 

9 

$12.75 
9 

$14.75 
9 

$82.86 
8 

31.  At  $2.25  a  yard,  how  much  will  2  yd.  of  silk  cost  ? 

32.  At  $3.25  each,  how  much  will  7  desks  cost  ?  , 

33.  At  $6.50  each,  how  much  will  6  tables  cost? 

34.  At  $7.35  each,  how  much  will  8  boys'  suits  cost  ?    . 


174  MULTIPLICATION 

ORAL  EXERCISE 

1.  How  much  is  10  x  2?  10  x  20? 

2.  To  multiply  by  10,  how  many  zeros  do  you  annex  ? 

3.  How  much  is  10  x  25?  10  x  47? 

Multiply  hy  10: 

4.  7         70        73        26         27        33         82         52 

5.  34        48        29        66         87        41         79         99 

6.  How  much  is  10  x  |3  ?  10  x  $3.00  ? 

7.  How  much  is  10  x  $7  ?  10  x  $7.50  ? 

8.  How  much  is  10  x  |15?  10  x  $15.75? 

9.  How  much  is  10  x  $21.50  ?  10  x  $100  ? 


Multiplying  by  Tens.  To  multiply  hy  10,  annex  a  zero. 
If  there  is  a  decimal  point,  move  it  one  place  to  the  right. 

Thus  10  X  75  =  750,  and  10  x  $7.50  =  $75.00. 

The  result  of  both  10  x  $3  and  10  x  $3.00  is  $30.  We  may  write 
this  as  $30,  or  as  $30.00.  The  product  of  10  x  $1.25  is  $12.50,  not 
$12.6,  it  being  the  custom  to  put  a  zero  at  the  right  in  such  a  case. 

To  multiply  hy  100,  annex  two  zeros.  Move  any  decimal 
point  two  places  to  the  right. 

To  multiply  hy  20,  multiply  hy  2  and 
annex  a  zero. 

To  multiply  hy  200,  multiply  hy  2  and 
annex  two  zeros. 

We  write  the  numbers  and  express  the  work  as  shown 
above  in  the  multiplication  of  25  by  20  and  of  32  by  300. 


MULTIPLYING  BY  TENS  175 

WRITTEN  EXERCISE 

Multiply  hy  10 : 

1.  $2.75  $12.75  $22.75  $25.50 

2.  $26.00  $48.30  $53.25  $69.73 

3.  $82.96  $100.00  $200.00  $500. 

Multiply  ly  20: 

4.  42      36  81  53  67 

5.  39               $1.20  $2.20  $3.50  $2.23 

6.  $4.50          $5.70  $4.90  $7.75  $9.65 

Multiply  hy  100 : 

7.  4    22    45    50    81    75    42    86 

8.  77   36    83    87    63    66    29    99 

Multiply  hy  200  : 

9.  5        8  7  9  6  15         18        25 

10.  35      41         48         55         46         60         67        75 

11.  At  $2  each,  how  much  will  30  chairs  cost? 

12.  At  $3  each,  how  much  will  40  tables  cost  ? 

13.  At  $5  each,  how  rauch  will  50  desks  cost  ? 

14.  At  $6  each,  how  much  will  70  coats  cost  ? 

15.  At  $32  each,  how  much  will  20  bedroom  sets  cost  ? 

16.  At  $60  each,  how  much  will  30  cows  cost? 

17.  At  $3.50  each,  how  much  will  20  hats  cost? 

18.  At  $17.50  each,  how  much  will  20  office  desks  cost? 

19.  At  $22.75  each,  how  much  will  30  overcoats  cost? 


176  MULTIPLICATION 

WRITTEN  EXERCISE 

1.  How  much  will  10  doB.  pencils  cost  at  30^  a  dozen? 
at  36^  a  dozen?  at  42^  a  dozen? 

2.  How  much  will  10  boxes  of  crayons  cost  at  35^  a 
box?  at  38(^  a  box?  at  43(^  a  box? 

3.  At  10^  apiece,  how   much  will  2  doz.  blackboard 
pointers  cost?   How  much  will  3  doz.  cost? 

4.  At  10^  a  small  package,  how  much  will  half  a  dozen 
small  packages  of  pens  cost  ? 

5.  How  many  fingers  have  the  pupils  in  a  class  of  27  ? 
How  many  toes  ?   How  many  fingers  and  toes  ? 

6.  If  an  arithmetic  costs  35^,  how  much  must  be  paid 
for  10  arithmetics  ?  for  2  arithmetics  ? 

7.  If  a  book  costs  $1.25,  how  much  must  be  paid  for 
10  such  books  ?  for  20  such  books  ?  for  30  such  books  ? 

8.  At  $12.75  each,  how  much  must  a  dealer  pay  for  40 
suits  of  boys'  clothes  ?  for  60  suits  ? 

9.  At  $38.25  each,  how  much  must  a  dealer  pay  for  30 
bedroom  sets  ?  for  40  sets  ?  for  60  sets  ? 

10.  At  $62.50  an  acre,  how  much  must  a  farmer  pay  for 
80  acres  of  land  ?  for  90  acres  ?  for  70  acres  ? 

11.  At  $45.50  each,  how  much  must  a  furniture  dealer 
pay  for  50  dining-room  sets?  for  20  sets?  for  40  sets? 

12.  At  $37.75  each,  how  much  must  a  dealer  pay  for  80 
office  desks  ?  for  70  desks  ?  for  30  desks  ? 

13.  At  $87.50  each,  how  much  must  a  dealer  pay  for  20 
Texas  ponies  ?   for  30  Texas  ponies  ? 


TWO-FIGURE  MULTIPLIER  177 

Two-Figure  Multiplier.    To  multiply  35  by  21,  we  write 
the  numbers  as  here  shown. 

We  first  multiply  by  1,  the  product  being  35. 
We  write  the  5  below  the  ones. 

We  then  multiply  by  2  tens,  the  product 
being  70  tens.  We  write  this  so  that  the 
right-hand  figure  (0)  is  below  the  multipher  (2), 
in  the  tens'  place. 

Adding,  the  total  product  is  735. 

WRITTEN  EXERCISE 

1.  At   $32  each,  how  much  will  a  merchant  pay  for 
21  suits  of  clothes?  for  31  suits? 

2.  At  $43  each,  how  much  will  a  dealer  pay  for  21  bed- 
room sets?  for  31  sets?  for  41  sets? 

3.  Multiply  by  21: 

46       53       65       76       83       38       52       94       60 

4.  Multiply  by  31  and  by  41,  in  turn : 

27       52       74       39       85       41       28       63       96 

Multiply  hy  S2,  62,  and  72,  in  turn : 


5.  33       46       57       44 

35       68       55 

79       82 

6.  47       69       25       71 

93       36       84 

58       95 

Multiply  the  following  : 

7.  63  X  95             63  X  84 

83x88 

93x97 

8.  74  X  96             84  X  98 

94x99 

64x88 

178 


MULTIPLICATION 


Two-Figure  Multiplier.     To  multiply  $2.75  by  54,  we 
write  the  numbers  as  here  shown. 

We  multiply  in  the  usual  way,  first  by  4 
units  and  then  by  5  tens. 

In  the   product   we   place   the   decimal 
point  between  dollars  and  dimes. 

The  product  is  $148.50. 

Teachers  who  feel  that  the  class  needs  a  more  com- 
plete explanation  may  refer  back  to  page  172. 


WRITTEN  EXERCISE 


Multiply  the  folloiving : 

1.  $4.82  by  15.        6. 

2.  $4.09  by  19. 

3.  $2.81  by  38. 

4.  $2.99  by  27. 

5.  $0.69  by  73. 


11.  $3.27  by  62. 

12.  $3.96  by  28. 

13.  $1.39  by  39. 

14.  $1.75  by  68. 

15.  $0.75  by  89. 


..23  by  12. 

7.  $2.17  by  32. 

8.  $3.41  by  29. 

9.  $4.80  by  36. 
10.  $5.60  by  71. 

16.  At  $24  a  dozen,  how  much  will  24  silver  tablespoons 
cost  ?  How  much  will  24  doz.  cost  ? 

17.  At  $36  a  dozen,  how  much  must  a  dealer  pay  for 
4  cut-glass  vases  ?  for  26  doz.  ?   for  15  doz.  ? 

18.  At  $7  each,  how  much  will  12  armchairs  cost  ?  What 
will  be  the  cost  of  25  ?  of  38  ?  of  46  ? 


Multiply  the  following : 

19.  23  X  $2.56.         22.  41  x  $3.45. 

20.  28  X  $3.91.  23.  43  x  $3.05. 

21.  75  X  $4.00.  24.  75  x  $4.50. 


25.  52  X  $2.86. 

26.  75  X  $3.08. 

27.  36  X  $5.50. 


TWO-FIGURE  MULTIPLIER  179 

WRITTEN  EXERCISE 

In  solving  these  examjjles  in  multiplication  see  how  large 
a  score  you  can  make  in  five  minutes,  counting  every  correct 
result  i,  and  subtracting  2  for  every  incorrect  result : 

1.  2.  3.  4.  5.  6. 

$2.50        $3.65        $4.80        $5.25        $12.50        $27.62 
31  22  34  42  44  20 


7. 

8. 

9. 

10. 

11. 

12. 

$4.60 

$7.95 

$5.92 

$9.37 

$13.75 

$52.96 

22 

26 

36 

39 

64 

30 

13. 

14. 

15. 

16. 

17. 

18. 

$5.80 

$8.34 

$8.75 

$9.99 

$48.70 

$99.99 

75 

27 

48 

99 

82 

90 

19.  A  clothing  dealer  bought   75  suits   of   clothes   at 
$12.25  each.   How  much  did  he  pay  for  the  lot? 

20.  A  dealer  bought  48  automobiles  at  $427.50  each. 
How  much  did  he  pay  for  the  lot? 

Multij^ly  the  following : 


21. 

22. 

23. 

24. 

25. 

$425.25 
32 

$275.05 
34 

$162.73 
36 

$421.11 
71 

$228.96 
30 

26. 

27. 

28. 

29. 

30. 

$326.45 

28 

$241.36 
35 

$432.47 
26 

$225.25 
88 

$600.09 
80 

180 


MULTIPLICATION 


Three-Figure  Multiplier.  1.  A  city  dealer  buys  234  auto- 
mobiles at  $348  per  car.    How  much  do  the  cars  cost  him? 

We  see  that  we  must  multiply  |348by234. 

We  multiply  by  4,  and  write  the  product, 
1392,  so  that  the  right-hand  figure  (2)  is  in 
the  ones'  place.  We  then  multiply  by  3,  and 
write  the  product,  1044,  so  that  the  right- 
hand  figure  (4)  is  in  the  tens'  place. 

We  then  multiply  by  2,  and  write  the 
product,  696,  so  that  the  right-hand  figure 
(6)  is  in  the  hundreds'  place. 

The  product  is  $81,432,  and  this  is  the  cost  of  the  cars 

2.  If  the  dealer  buys  240  cars  at  $720 
each,  how  much  do  all  the  cars  cost  him? 

To  multiply  by  240  is  the  same  as  to 
multiply  by  10  x  24.  We  multiply  by  10 
by  annexing  0,  and  so  we  may  multiply 
$720  by  24  and  annex  0  as  here  shown. 

The  product  is  $172,800,  the  total  cost. 


$720 

240 
28800 
1440 
$172800 


WRITTEN  EXERCISE 


Multiply  the  folloiving 


1. 

2. 

3. 

4. 

5. 

6. 

231 

231 

439 

575 

$575 

$356 

111 

123 

123 

,222 

322 

550 

7. 

8. 

9. 

10. 

11. 

12. 

243 

348 

329 

426 

$527 

$481 

126 

241 

423 

178 

136 

670 

THREE-FIGURE  MULTIPLIER 


181 


Multiplication  Continued.    A  maker  sells  204  wagons  at 
$116.67  per  wagon.    How  much  money  does  he  receive? 

We  see  that  he  receives  204  x  $116.67. 

We  multiply  as  on  page  180,  except 
that  there  is  no  need  to  multiply  by  0. 

We  multiply  by  4,  and  write  the 
product,  46668,  so  that  the  right-hand 
figure  (8)  is  in  the  ones'  place.  We  mul- 
tiply by  2,  and,  because  we  are  multiply- 
ing by  hundreds,  we  write  the  product 
so  that  the  right-hand  figure  (4)  is  in  the  hundreds'  place. 

The  product  is  $23,800.68,  and  this  is  the  money  received. 

The  pupils  are  already  familiar  with  multiplication  involving  money,  and 
they  know  where  to  place  the  decimal  point. 


$116.67 
204 
466  68 
23334 

$23800.68 


WRITTEN  EXERCISE 

1.  At  $85  an  acre,  how  much  must  a  farmer  pay  for 
104  acres  of  land  ?  for  107  acres  ?  for  109  acres  ? 

2.  At  $37.50  a  head,  how  much  will  102  head  of  cattle 
cost?  143  head?  107  head?  109  head? 


Multiply 

the  folloicing 

•' 

3. 

4. 

5. 

6. 

7. 

$481.20 

$502.75 

$681.39 

$217.42 

$321.50 

104 

109 

102 

206 

371 

8. 

9. 

10. 

11. 

12. 

$491.76 

$482.75 

$536.47 

$671.70 

$879.90 

381 

243 

308 

426 

897 

182  ■      MULTIPLICATION 

REVIEW  DRILL 

Find  the  cost  of  the  following : 

1.  6  books  at  31^.  13.  8  yd.  of  carpet  at  70^. 

2.  3  lb.  of  tea  at  42^.  14.  5  cans  of  cocoa  at  41^. 

3.  4  cows  at  $41.  15.  9  gallons  of  oil  at  21^. 

4.  6  lb.  of  steak  at  21  f  16.  7  tennis  balls  at  20 (^. 

5.  7  collars  at  21^.  17.  3  writing  tablets  at  15^. 

6.  6  flags  at  15f  18.  7  lb.  of  butter  at  30(^. 

7.  6  lb.  of  figs  at  15 (^.  19.  2  bu.  of  wheat  at  90  (^. 

8.  12  pencils  at  3^.  20.  8  lb.  of  walnuts  at  15^. 

9.  9  lb.  of  meat  at  20  f  21.  21  yd.  of  ribbon  at  9^. 

10.  15  trout  flies  at  8^.         22.  3  lb.  of  cheese  at  32  f 

11.  9  lb.  of  sugar  at  6^.        23.  18  doz.  buttons  at  5^. 

12.  9  cans  of  soup  at  12^.     24.  4  sewing  machines  at  $42. 

Find  the  cost  of  the  following ,  and  the  change  due: 

25.  6  lb.  of  roast  beef  at  20(^.   Paid  $1.25. 

26.  7  writing  tablets  at  12  f    Paid  $1. 

27.  2  pencils  at  5^  and  3  tablets  at  12^.    Paid  50^. 

28.  3  cows  at  $40  and  2  sheep  at  $6.    Paid  $140. 

29.  2  horses  at  $125  and  a  carriage  at  $100.    Paid  $400. 

30.  5  acres  of  land  at  $90  and  2  acres  at  $50.    Paid  $600. 

31.  7  cows  at  $50  and  6  cows  at  $40.   Paid  $600. 

32.  5  tables  at  $15  and  20  desks  at  $4.   Paid  $160. 

33.  8  chairs  at  $2  and  a  table  at  $9.    Paid  $30. 

Ex8.  1-24  may  be  taken  for  oral  work. 


USING  WHAT  YOU  HAVE  LEAENED 


183 


V.   USING  WHAT  YOU  HAVE  LEARNED 
BUYING  PRESENTS  FOR  CHRISTMAS 

1.  If  some  children  pay  45  (^  for  a  Christmas  tree  and 
give  the  dealer  50^,  how  much  change  is  due  ? 


2.  If  Maude  buys  9  candy  canes,  at  8^  each,  how  much 
do  they  cost  ?   How  much  change  should  she  get  from  75^  ? 

3.  If  MolHe  buys  her  mother  4  handkerchiefs  at  25^ 
each,  how  much  do  they  cost? 

4.  If  Jack  buys  10  colored  balls  at  4^  each,  how  much 
do  they  cost? 

5.  Sue  buys  5  strings  of  tinsel  at  12^  a  string.    How 
much  does  the  tinsel  cost? 

6.  How  much  will  2  doz.  candles  cost  at  18^  a  dozen  ? 

7.  The  children  bought  some  toys   costing  10^,   20^, 
32(^,  30.^,  10(^,  25f    How  much  did  these  all  cost? 


184  USING  WHAT  YOU  HAVE  LEARNED 

GOING  TO  THE  PQST  OFFICE 

1.  It  costs  2^  for  a  stamp  for  a  letter  weighing  1  oz.  or 
less.   How  much  will  stamps  for  a  dozen  letters  cost  ? 

In  the  examples,  each  letter  may  be  taken  as  weighing  1  oz. 

2.  A  postal  card  costs  1^.  How  much  will  it  cost  you 
to  buy  a  half  dozen  postal  cards  and  8  stamps  for  letters  ? 

3.  If  you  have  a  friend  living  in  Italy,  a  postage  stamp 
for  a  letter  to  be  sent  there  will  cost  5^.  How  much  will 
it  cost  for  postage  if  you  write  a  letter  every  month  for 
the  twelve  months  of  a  year  ? 

4.  If  you  send  a  newspaper  by  mail,  the  postage  is  1^ 
for  each  4  oz.  or  less.  How  much  will  it  cost  to  send  a 
letter,  3  postal  cards,  and  a  newspaper  weighing  4  oz.  ? 

5.  You  can  send  parcels  through  the  post  office.  If  your 
cousin  lives  about  100  miles  away,  and  you  wish  to  send 
him  a  book  weighing  2  lb.,  the  postage  will  be  6^.  How 
much  will  it  cost  to  send  him  such  a  book,  a  letter,  and 
a  newspaper  as  heavy  as  the  one  in  Ex.  4  ? 

6.  If  you  are  in  a  hurry  to  have  your  letter  delivered, 
you  may  put  on  a  special-deHvery  stamp,  costing  100, 
besides  the  postage  on  the  letter.  How  much  will  it  cost 
you  to  send  a  special-delivery  letter? 

7.  If  you  are  sent  to  the  post  office  to  buy  2  doz.  2-cent 
stamps,  5  postal  cards,  and  a  special-delivery  stamp,  how 
much  money  must  you  take  with  you? 

The  pupils  should  be  asked  to  state  problems  from  their  own  experience 
similar  to  the  above. 


PROBLEMS  185 

A  DAY  IN  THE  CITY 

1.  Irene's  father  took  her  to  the  city.  Their  railroad 
tickets  cost  |2.10.  They  paid  50^  for  street-car  fares  and 
$1.50  for  luncheon.  They  paid  75^  for  a  cab  to  make 
a  call.   How  much  money  did  they  spend  ? 

2.  Irene's  father  gave  her  the  money  for  some  Christ- 
mas presents.  She  bought  a  doll  for  $1.25,  a  pair  of  skates 
for  $1.50,  a  bat  and  a  glove  to  give  to  her  brother  Fred 
for  $1.25,  and  some  handkerchiefs  for  her  mother  for  75^. 
How  much  did  she  spend  in  all  ? 

3.  At  a  fruit  stand  Irene  saw  the  sign,  "Apples,  3  for 
5^."    How  many  apples  could  she  buy  for  10^? 

4.  Irene's  father  owed  three  bills  in  the  city.  The 
amounts  were  $125,  $16.50,  and  $48.25.  She  went  with 
him  when  he  paid  them.    How  iriuch  did  he  pay  in  all  ?   '  <>  ' 

5.  Irene's  father  sent  a  telegram  of  16  words.  It  cost 
him  40^  for  the  first  ten  words,  and  3^  for  each  additional 
word.    How  much  did  he  pay  for  sending  the  telegram?  /^ 

6.  Irene  did  some  shopping  for  her  mother.  She  bought 
two  pairs  of  gloves  at  $1.50  a  pair,  and  three  handkerchiefs 
at  25^  each.    How  much  did  she  pay  for  them  all?       >   / 

7.  Irene's  father  bought  for  her  brother  Fred  a  story 
book  costing  75^,  a  tennis  racket  costing  $1.50,  and  a 
ball  costing  45^.    How  much  did  all  three  cost  ?^''.^,y  ^^ 

8.  A  football  team  in  their  town  had  asked  IreneV 
father  to  find  what  their  suits  would  cost.  He  found  that 
the  price  was  $3.50  each.  How  much  will  11  suits  cost? 
How  much  will  22  suits  cost? -5     36tSO  . 


186  USING  WHAT  YOU  HAVE  LEARNED 

REVIEW  DRILL 

Multiply  the  following : 


1. 

37  X  96. 

24. 

4  X  $12.75. 

47. 

32  X  $11.48. 

2. 

48  X  74. 

25. 

6  X  $31.76. 

48. 

46  X  $12.87. 

3. 

66  X  89. 

26. 

8  X  $96.43. 

49. 

84  X  $21.96. 

4. 

76  X  846. 

27. 

7  X  $86.52. 

50. 

34  X  $28.47. 

5. 

87  X  987. 

28. 

5  X  $77.77. 

51. 

37  X  $39.05. 

6. 

49  X  757. 

29. 

9  X  $65.78. 

52. 

40  X  $37.62. 

7. 

86  X  848. 

30. 

50  X  $6.70. 

53. 

26  X  $48.37. 

8. 

79  X  837. 

31. 

82  X  $4.48. 

54. 

32  X  $61.76. 

9. 

47  X  563. 

32. 

72  X  $6.93. 

55. 

56  X  $82.78. 

10. 

80  X  909. 

33. 

84  X  $4.72. 

56. 

29  X  $70.06, 

11. 

86  X  876. 

34. 

73  X  $6.48. 

57. 

36  X  $72.83, 

12. 

43  X  907. 

35. 

66  X  $4.96. 

58. 

48  X  $86.96. 

13. 

139  X  462. 

36. 

54  X  $3.97. 

59. 

57  X  $91.87, 

14. 

823  X  823. 

37. 

27  X  $8.71. 

60. 

67  X  $75.78, 

15. 

237  X  409. 

38. 

42  X  $6.77. 

61. 

49  X  $81.96, 

16. 

207  X  439. 

39. 

73  X  $9.75. 

62. 

73  X  $29.78, 

17. 

342  X  826. 

40. 

54  X  $8.44. 

63. 

82  X  $41.86. 

18. 

436  X  896. 

41. 

38  X  $7.62. 

64. 

67  X  $92.98, 

19. 

525  X  687. 

42. 

87  X  $7.56. 

65. 

76  X  $87.46, 

20. 

426  X  839. 

43. 

43  X  $8.91. 

66. 

64  X  $37.92, 

21. 

672  X  678. 

44. 

57  X  $5.40. 

67. 

59  X  $89.98, 

22. 

420  X  745. 

45. 

75  X  $8.60. 

68. 

65  X  $56.68 

23. 

630  X  820. 

46. 

86  X  $9.55. 

69. 

91  X  $37.48 

DIVISION 


187 


VI.   DIVISION 
ORAL  EXERCISE 

1.  How  many  lO's  are  there  in  20  ?  in  30  ?  in  150  ? 

2.  Do  you  see  an  easy  way  of  dividing  by  10  ? 

3.  Divide  each  of  these  numbers  by  10 : 

160        210        230        340        480        560        750 

4.  How  many  2's  in  4  ?   How  many  20's  in  40  ? 

5.  Do  you  see  an  easy  way  of  dividing  by  20  ? 


Dividing  by  10»s.  In  dividing  240  by  20 
we  may  cancel  the  O's  in  20  and  240,  and 
simply  divide  24  by  2  as  here  shown. 

The  quotient  is  12. 


1.  Divide  by  20 : 
120        140 

Divide  hy  30: 

2.  120        240 

3.  510         570 


WRITTEN  EXERCISE 


180 
360 

630 


260    380    540   780 


390 
690 


Divide  the  following : 

4.  480^40.     8.  720 -J- 60. 

5.  560^40.     9.  960-5-60. 

6.  750-4-50.     10.  1440-60. 

7.  360  -  60.     11.  2340  -  90. 


420 
720 


450 
810 


480 
960 


12.  2870  -  70. 

13.  1400^70. 

14.  1400-700. 

15.  9600-4-800. 


188 


DIVISION 


Fraction  in  the  Quotient.  If  we  divide  4162  by  3,  we  find 
that  the  quotient  is  1387  with  a  remainder  of  1.  If  we 
divide  this  remainder,  1,  by  3,  we  have  J. 
We  write  this  J  in  the  quotient. 

The  number  by  which  we  divide  is  called 
the  divisor. 

The  number  divided  is  called  the  dividend. 

The  result  of  division  is  called  the  quotient. 

The  dividend  is  the  product  of  the  divisor  and  the  quotient. 

If  we  divide  4163  by  10,  we  see  that 
the  remainder  is  3,  the  last  figure  in  the 
number  divided.  We  write  the  work  as 
here  shown. 

WRITTEN  EXERCISE 

quotients,  and  write  the  remainders  as  fractions : 


Find  the  qu 

1. 

2743- 

-3. 

2. 

4173- 

-4. 

3. 

6131- 

^-5. 

4. 

4237- 

-6. 

5. 

8195- 

-7. 

6. 

2575- 

-8. 

7. 

3241- 

-9. 

8. 

6871- 

-5. 

9. 

8233- 

-4. 

10. 

4673- 

-8. 

11. 

6793  H 

-4. 

12.  4127-^2. 

13.  8345-6. 

14.  9281^5. 

15.  8196-7. 

16.  4237-8. 

17.  3496-9. 

18.  7843-6. 

19.  8207  -  5. 

20.  3267-8. 

21.  9725-6. 

22.  4195-9. 


23.  6464-9. 

24.  5072-3. 

25.  4352-7. 

26.  8773-5-8. 

27.  5225-4. 

28.  8231-10 

29.  6243  -  10 

30.  9187  -  10 

31.  2983  -  10 

32.  3761  -  10 

33.  3767-10, 


PEEPAEATION  FOR  LONG  DIVISION  189 

ORAL  EXERCISE 

1.  How  much  is  8  X  10  ?    80  -^  8  ?   80  ^  10  ? 

2.  How  much  is  8  x  11  ?    88  -  8  ?    88  ^  11  ? 

3.  How  much  is  10  X  11  ?    110-10?    110-11? 

State-  the  following  products  and  quotients: 


4.  7  X  11 

77-7 

77-11 

99-11 

5.  6  X  11 

66-6 

66-11 

55-^11 

6.  4  X  11 

44-4 

44-11 

33-11 

7.  If  we  divide  22  by  11,  what  is  the  quotient? 

8.  If  we  divide  23  by  11,  what  is  the  quotient  and  what 
is  the  remainder  ? 

Divide  each  of  the  following  numbers  hy  11,  stating  the 
quotient  and  also  the  remainder,  if  any : 


9.  33 

34 

35  . 

37 

39 

40 

10.  44 

46 

47 

49 

50 

54 

11.  66 

69 

70 

71 

73 

76 

12.  88 

89 

91 

93 

95 

97 

13.  22 

220 

330 

331 

^  442 

556 

14.  55 

550 

660 

661 

'  777 

441 

15.  If  the  school  has  to  pay  $11  for  a  teacher's  desk, 
how  many  desks  can  it  buy  for  $25,  and  how  much  money 
willit  have  left? 

16.  If  the  school  has  to  pay  $4  for  a  pupil's  desk,  how 
many  desks  can  it  buy  for  $25,  and  how  much  money  will 
it  have  left? 


190  DIVISION 

17.  If  a  dealer  in  school  desks  has  to  pay  $3  for  a  pupil's 
desk,  how  do  you  find  how  many  desks  he  can  buy  for  $200, 
and  how  much  money  he  will  have  left  ? 

The  pupil  is  not  expected  to  perform  the  operation  mentally.  The  pur- 
pose of  this  oral  question  and  of  those  immediately  following  is  to  lead 
him  to  see  the  importance  of  extending  his  knowledge  to  long  division. 

18.  If  the  dealer  mentioned  in  Ex.  17  has  to  pay  $11  for 
a  teacher's  desk,  and  has  $200  with  which  to  buy  a  number 
of  such  desks,  how  do  you  find  how  many  desks  he  can 
buy  for  $200,  and  how  much  money  he  will  have  left? 
Can  you  do  this  work  yet  ?  Could  you  do  it  if  the  price  of 
each  desk  was  $10  instead  of  $11  ? 

Divide  such  of  the  following  numbers  hy  11  as  you  can 
easily  divide  without  pencil  and  paper ,  and  write  the  others 
down  on  paper  and  divide  them  after  you  have  studied  the 
next  page : 

1100  2200  3300 

4400  5555  6600 

7700  8877  9900 

7705  5507  6609 

7810  6831  7296 

6666  6644  4466 

2244  4422  2288 

3430  3443  3454 

5500  5610  5621 

8800  8811  8921 

9999  9911  8932 


19. 

11 

110 

20. 

44 

440 

21. 

77 

770 

22. 

24 

221 

23. 

98 

•  451 

24. 

66 

660 

25. 

22 

220 

26. 

33 

330 

27. 

55 

551 

2d. 

88 

883 

29. 

99 

997 

Written  Work 

Check 

14 

14 

11)154 

11 

11 

14 

44 

14 

44 

154 

LONG  DIVISION  191 

Long  Division.  If  a  dealer  pays  $154  for  11  boys'  suits, 
how  much  does  he  pay  for  each  suit  ? 

For  each  suit  he  must  pay  $154  ^  11,  so  we  need  to  know 
how  to  divide  $154  by  11.  In  such  a  division  we  need  not 
write  the  dollar  sign  ($). 

The  following  shows  the 
work  which  we  do  : 

Divide,  15  h-  11 

Multiply,  1  X  11 

Subtract ;  then  44  h-  11 

Multiply,  4  X  11 

Subtract ;  no  remainder 

The  teacher  should  take  up  this  work  on  the  blackboard,  explain  what 
is  done  in  each  step,  show  the  pupil  what  he  is  expected  to  write  (Written 
Work),  and  explain  the  check. 

WRITTEN  EXERCISE 

Divide  each  of  these  numbers  by  11 : 

1.  121.      4.  1221.      7.  1331.      10.  4741.  13.  2541. 

2.  132.      5.  1232.      8.  1441.      11.  3531.  14.  7887. 

3.  143.      6.  1551.      9.  3861.      12.  2332.  15.  1705. 

16.  At  $11  each,  how  many  football  suits  can  a  dealer 
buy  for  $715  ?   for  $726  ?   for  $836  ? 

17.  At  $11  each,  how  many  Boy  Scout  suits  can  a  dealer 
buy  for  $242  ?  for  $352  ?  for  $363  ? 

18.  If  11  girls  weigh  638  lb.,  what  is  their  average 
weight  ? 

The  idea  of  "  average  "  should  be  explained  to  the  class  if  necessary. 


192 


DIVISION 


Two-Figure  Divisor.  A  piano  manufacturer  sold  21  pianos 
for  $7161.    How  much  did  he  receive  for  each  piano? 

We  see  that  we  must  divide  |7161  by  21. 

Before  we  divide,  it  is  a  good  plan,  at  first,  to  write  out 
a  table  of  21 's,  as  follows  : 

1x21=21  4x21=84  7x21  =  147 

2x21  =  42  5x21  =  105  8x21  =  168 

3x21=63  6x21  =  126  9x21  =  189 

Such  tables  should  not  be  used  after  the  form  of  the  work  is  understood. 

We  see  that  we  have  first  to  divide  71  hundreds  by  21. 
From  the  table  we  see  that  3x21=63,  or8  less  than  71. 
So  we  know  that  71  hundreds  -^  21  =  3  hun- 
dreds, with  a  remainder  of  8  hundreds. 

We  therefore  write  the  3  in  the  hun- 
dreds' place  as  the  first  figiu-e  of  the 
quotient. 

The  remainder,  8  hundreds,  equals  80 
tens,  and  80  tens  +  6  tens  =  86  tens. 

From  the  table  we  see  that  4  x  21  =  84, 
which  is  2  less  than  §6.    So  we  know  that 
86  tens  -5-21  =  4  tens,  with  a  remainder  of 
2  tens,  or  20.   We  therefore  write  the  4  in  the  quotient, 
in  the  tens'  place. 

Then  20  -h  1  =  21,  still  to  be  divided.  21  -^  21  =  1,  and 
we  write  the  1  in  the  quotient,  in  the  ones'  place. 

The  quotient  is  then  341,  and  so  the  manufacturer 
received  $341  for  each  piano. 

To  check  the  answer,  21  x  $341  =  $7161. 


LONG  DIVISION  193 

ORAL  EXERCISE 

Divide  the  following  numbers  hy  21  and  state  the  quotient ; 
if  you  cannot  tell  the  quotient  readily,  divide  the  first  figure 
of  the  dividend  hy  the  first  figure  of  the  divisor : 

1.  42  63  84  168  126  147 

Divide  the  following  numbers  hy  41  and  state  the  quotient ; 
dividing  the  first  two  figures  of  the  dividend  hy  the  first  figure 
of  the  divisor : 

2.  205  123  164  246  287  369 

State  only  the  first  figure  in  the  quotient  : 

3.  462  -^  21.  6.  620  -  31.  9.   1230  -  41. 

4.  693-21.  7.  651-31.  10.  1271-41. 
5.399-21.             8.682-31.             11.1530-51. 


WRITTEN  EXERCISE 

Oil 

nde  the  following  : 

1. 

483-21.             6.  496-31. 

11. 

3024-21. 

2. 

945-21.             7.  943-41. 

12. 

1386-21. 

3. 

525-21.             8.  589-31. 

13. 

2079-21. 

4. 

2436-21.            9.  1147-31. 

14. 

2601-51. 

5. 

2793-21.         10.  5661-51. 

15. 

1491-71. 

16.  At  $21  a  dozen,  how  many  rifles  can  a  dealer  buy 
for  $504?  for  $693? 

17.  At  $31  a  dozen,  how  many  dozen  boys'  sweaters  can 
a  dealer  buy  for  $651?  for  $961? 


194  DIVISION" 

Long  Division  Continued.  To  divide  3328  by  32  we  write 
the  numbers  as  here  shown. 

We  see  that  33  hundreds  -5-  32  =  1  hun- 
dred, with  a  remainder  of  1  hundred. 

We  write  the  1  in  the  quotient  in  the 
hundreds'  place. 

Bringing  down  the  next  figure,  2  (tens), 
we  have  12  tens  to  be  divided  by  32. 

But  12  does  not  contain  32,  so  we  write 
0  in  the  quotient  in  the  tens'  place. 

Bringing  down  the  next  figure,  8,  we  have  128  to  be 
divided  by  32. 

128  -^  32  =  4,  and  we  write  the  4  in  the  ones'  place. 

The  quotient  is  104. 

WRITTEN  EXERCISE 

Divide  the  following: 

1.  1302  ^  21.           5.  6363  ^  21.  9.  4824  h-  12. 

2.  1224  -i- 12.           6.  6384  ^  12.  10.  2442  ^  22. 

3.  3840  ^  32.           7.  2142  -^  42.  11.  5304  h-  52. 

4.  3844  -^  62.           8.  3968  -  62.  12.  7344  ^  72. 

13.  A  manufacturer  receives  $6882  for  a  number  of 
canoes,  each  canoe  selhng  at  |31.  How  many  canoes  does 
he  sell? 

14.  A  dealer  pays  $2398  for  a  number  of  bicycles,  each 
bicycle  costing  |22.   How  many  bicycles  does  he  buy  ? 

15.  A  dealer  buys  a  lot  of  young  Shetland  ponies  for  $72 
apiece.   He  pays  |7704.   How  many  ponies  does  he  buy? 


LONG  DIVISION 


195 


Long  Division  Continued.  To  divide  4510  by  79  we  write 
the  numbers  as  here  shown. 

At  first  we  might  think  that,  because 
45  -5-  7  =  6  and  a  remainder,  the  first  fig- 
ure in  the  quotient  should  be  6.  But  this 
would  be  too  large,  as  we  should  find, 
because  6  x  79  =  474,  which  is  larger 
than  451. 

We  see  that  79  is  nearly  80,  and  so  we 
see  that  we  can  find  the  first  figure  more 
easily  by  thinking  of  45  ^  8  than  by  thinking  of  45  -5-  7. 

In  division,  no  product  should  he  larger  than  the  number 
above  it;  no  remainder  after  any  subtraction  should  be  larger 
than  the  divisor. 

Now,  dividing  in  the  usual  way,  we  find  that  the  quotient 
is  57  and  that  there  is  a  remainder  of  7.  It  is  customary 
to  write  the  result  57^'^. 


WRITTEN  EXERCISE 


Divide  the  following  : 

1.5929^49.            6.8172-^59.  11.4675-99. 

2.  3219  -^  29.            7.  2448  -  78.  12.  5183  -^  58. 

3.  1135^29.            8.  8636-98.  13.  5334-77. 

4.  2269-39.            9.  1585-99.  14.  6977-88. 

5.  4091  -  69.     10.  5155  -  37.  15.  6363  -  96. 

16.  A  dealer  pays  $6375  for  some  sailboats  at  $75  each. 
How  many  boats  does  he  buy  ? 


196 


DIVISION 


WRITTEN  EXERCISE 

Divide,  and  check  the  work  hy  multiplying : 

1.  189^21.       6.  328-41.  11.  648^81. 

2.  637-^91.       7.  639-^71.  12.  488^61. 

3.  224  ^  32.       8.  416  -^  52.  13.  504  ^  72. 

4.  498  -  83.       9.  438  -  73.  14.  837  -  93. 

5.  236  -  59.      10.  553  -  79.  '   15.  792  ^  99. 


Divide,  writing  "remainder''  after  each  remainder: 


16.  2706- 

-41. 

24. 

3366- 

-51. 

32. 

6461- 

-71 

17.  5368- 

-61. 

25. 

6238- 

-81. 

33. 

6647^ 

-91 

18.  6724- 

-82. 

26. 

9568- 

-92. 

34. 

5084^ 

-62 

19.  7447- 

-73. 

27. 

3498. 

-53. 

35. 

9504^ 

-72 

20.  7614- 

-94. 

28. 

6809  - 

-84. 

36. 

3569-^ 

-29 

21.  6434- 

-59. 

29. 

7345- 

-65. 

37. 

8148^ 

-74 

22.  2464- 

-22. 

30. 

5346- 

-22. 

38. 

3366^ 

-66 

23.  5475- 

-77. 

31. 

9639- 

-44. 

39. 

3905^ 

-55 

Divide, 

using 

fractions 

insteac 

I  of  remainders 

.  ; 

40.  4872- 

-56. 

47. 

3441- 

-37. 

54. 

3655^ 

-43 

41.  2697- 

-93. 

48. 

8579- 

-73. 

55. 

2576 -f 

-92 

42.  3648- 

-32. 

49. 

8957- 

-79. 

56. 

9853-* 

-49 

43.  8512- 

-76. 

50. 

7319- 

-53. 

57. 

7369^ 

-52 

44.  8556- 

-23. 

51. 

8609- 

-61. 

58. 

9423^ 

-63 

45.  5110- 

-14. 

52. 

6891- 

-31. 

59. 

6578 -* 

-74 

46.  5248- 

-64. 

53. 

3954- 

-23. 

60. 

6457- 

-59. 

LONG  DIVISION  ,  197 

WRITTEN  EXERCISE 

1.  If  a  farmer  pays  |1935  for  43  head  of  cattle,  how 
much  does  he  pay  a  head  ? 

2.  An  agent  sells  23  sewing  machines  for  $483.   How 
much  does  he  receive  for  each  ? 

3.  The  school  attendance  for  23  days  in  our  room  was 
805.    What  was  the  daily  attendance  ? 

4.  A  city  dealer  bought  25  children's  bicycles  for  $275. 
How  much  did  they  cost  apiece  ? 

5.  At  $71  each,  how  many  Texas  ponies  can  be  bought 
for  $1491  ?   How  many  can  be  bought  for  $1562  ? 

6.  An  express  train  ran  559  miles  in  13  hr.    What  was 
the  rate  per  hour  ? 

7.  How  many  street  cars,  each  carrying  72  persons,  will 
it  take  to  carry  3312  persons  ? 

8.  A  buyer  paid  $2112  for  64  cows.    How  much  was 
that  for  each  cow  ? 

9.  How  many  hours  will  it  take  an  automobile  to  go 
1254  miles,  if  it  goes  at  the  rate  of  19  miles  an  hour? 

10.  A  man  has  $1275  with  which  to  purchase  cows.  At 
$55  apiece,  how  many  cows  can  he  buy,  and  how  much 
money  will  he  have  left  ? 

Divide  the  following : 

11.  38,178^63.      14.  78,408-99.  17.  69,375-75. 

12.  30,456  -  94.   15.  84,864  -  52.  18.  89,568  -  96. 

13.  26,896  -  82.   16.  54,432  -  84.  19.  37,950  -  75. 


198 


DIVISION 


Dividing  Dollars  and  Cents.    1.  A  man  paid  $5  for  four 
sleds  for  his  boys.    How  much  did  he  pay  for  each  sled  ? 

Each  sled  cost  J  of  $5,  or  $5  h-  4,  so  we  must  know 
how  to  divide  $5  by  4. 

We  write  $5.00  for  $5  and  divide  jiist 
as  we  do  with  other  numbers,  placing  the 
decimal  point  in  the  quotient  exactly  below 
the  decimal  point  in  the  dividend. 

The  quotient  is  $1.25,  so  he  paid  $! 

2.  A  dealer  paid  |28.35  for  21  sleds. 
pay  for  each  sled  ? 

Each  sled  cost  $28.35  ^  21. 

We  divide  just  as  we  do  with  other 
numbers,  placing  the  decimal  point  in 
the  quotient  exactly  above  the  decimal 
point  in  the  dividend.  The  quotient  is 
$1.35,  so  he  paid  $1.35  for  each  sled. 

We  check  our  work  by  multiplying 
$1.35  by  21,  the  result  being  $28.35. 


.25  for  each  sled. 
How  much  did  he 


WRITTEN  EXERCISE 


Divide  the  following : 


1.  $7^5. 

5.  $5.40^12. 

9.  $32.40^12. 

2.  $2.70  H-  5. 

6.  $5.40-^15. 

10.  $75.60  -^  14. 

3.  $15.12^7. 

7.  $5.04^14. 

11.  $15.12-*- 56. 

4.  $25.92-^9. 

8.  $8.64^27. 

12.  $25.92  ^  54. 

Some  schools  do  not  at  this  time  take  up  the  work  on  this  page.    The 
page  is  not  needed  for  the  regular  work  (except  page  199). 


PEOBLEMS  IN  LONG  DIVISION 


199 


WRITTEN  EXERCISE 

1.  A  farmer  in  Iowa  raised  9000  bu.  of  corn  on  72  acres. 
How  many  bushels  did  each  acre  average  ? 

The  word  "  average  "  should  again  be  explained  to  the  children,  if  neces- 
sary, together  with  the  expression  "  on  an  average  "  and  the  method  of 
finding  the  average  cost  of  several  articles. 

2.  A  laborer  earned  $70  in  28  days.    How  much  did  he 
earn  per  day  ? 

3.  A  family  spends  $468  for  groceries  in  a  year.    How 
much  is  that  a  week  ? 

In  all  such  cases  the  children  should  be  told  to  take  52  weeks  to  a  year, 
and  should  understand  that  the  average  expenditure  per  week  is  required. 

4.  An  electric-light  bill  was  $15.04  for  94  days.    How 
much  did  it  average  per  day  ? 

5.  Mary's  uncle  has  a  fine  herd  of  48  cows  valued  at 
$3600.    What  are  the  cows  worth  on  the  average  ? 

6.  If  an  automobile  dealer  sells  56  cars  for  $47,600, 
what  is  the  average  price  per  car? 

7.  If  a  family  pays  $364.80  for  food  in  96  days,  what 
is  the  average  cost  per  day? 

Divide,  giving  the  quotient,  and  the  remainder  if  any : 

8.  896  -  28.  14.  2450  -  50.  20.  $77  -  55. 
396^66.          15.  2450^-49. 
448-14.          16.  5292^98. 
272^-68.          17.  3087-98. 

18.  6897 


9 
10 
11 
12 
13 


528-22. 
630-21. 


57. 


19.  7872-82. 


21.  $46.80-78. 

22.  32,225  -  72. 

23.  41,005  -  67. 

24.  77,760  -  96. 

25.  80,976  -  84. 


200  FRACTIONS 

VII.   FRACTIONS 
ORAL  EXERCISE 

1.  Maud  needs  J  of  a  yard  of  cloth  for  a  doll's  dress. 
She  has  a  yard  of  cloth.  How  many  dresses  can  she 
make  from  it? 

2.  She  has  2  yd.  of  another  kind  of 'cloth.  How  many 
dresses,  of  the  kind  stated  in  Ex.  1,  can  she  make  from  it  ? 

3.  If  Maud  uses  J  of  a  piece  of  cloth  that  is  1^  yd.  long, 
what  part  of  a  yard  does  she  use?  Draw  a  line  on  the 
blackboard  to  represent  1^  yd.,  and  mark  off  ^  of  it. 

Teachers  should  recognize  that  the  object  of  such  a  problem,  as  of  this 
entire  page,  is  to  show  the  necessity  for  further  work  in  fractions.  It  is 
not  so  important  that  the  question  should  be  answered  promptly,  as  to  have 
the  pupil  feel  that  he  must  learn  more  about  fractions.  The  problems 
furnish  a  motive  for  progress. 

4.  Maud's  mother  gives  her  a  piece  of  cloth  16  in.  long 
and  tells  her  she  can  have  half  of  it.  Maud  says  that  even 
16  in.  is  not  enough,  but  that  she  needs  1^  times  as' much. 
How  do  you  find  how  much  Maud  needs?  Can  you  tell 
how  much  she  needs? 

5.  Maud's  mother  tells  her  that  she  has  a  piece  of  cloth 
30  in.  long  and  can  spare  her  all  but  6  in.  How  much  can 
Maud  have?  Is  this  as  much  as  she  needs  according  to 
Maud's  suggestion  in  Ex.  4  ? 

6.  For  trimming  some  dolls'  clothes  Maud  has  a  piece  of 
ribbon  6^  in.  long,  and  another  piece  of  the  same  kind 
5J  in.  long.  Allowing  a  loss  of  J  in.  for  sewing  the  pieces 
together,  how  long  a  piece  will  these  make  ? 


TEACTIONS 


201 


ORAL  EXERCISE 

1.  How  many  halves  in  1  apple?  in  IJ-  apples? 

2.  How  many  halves  in  2  apples?  in  21  apples?   in 
3^  apples  ?  in  4  apples  ? 

3.  How  many  whole  ap- 
ples in  1^  apples?  in  ^  apples? 
in  ^  apples  ?  in  -^  apples  ? 

4.  How  many  inches  are 
llin.  +  lin.?  llin.  +  ljin.? 
31  in.  + 11  in.?    31  in.  +  2  in.?    31  in.  +  21  in.? 

5.  If  Harriet  needs  21  yd.  of  cloth  for  some  sewing, 
and  has  31  yd.,  how  much  has  she  to  spare  ? 

State  the  results : 


6.  31  +  1 

8.  41  +  21 

10.  91-3. 

12.  81  +  41 

7.  31  +  31 

9.  71-1 

11.  61-31 

13.  81-41 

k 


B 


D 


E 


14.  Look  at  the  blocks  in  this  picture.  I)  is  what  part 
as  large  as  CI  i>  is  what  part  as  large  as  -B?  2>  is  what 
part  as  large  as  J.  ?  (7  is  what  part  as  large  as  ^  ? 


42 


'  3 


202  FRACTIONS 

Adding  Fractions.  If  Kate  buys  two  remnants  of  rib- 
bon, one  being  4|  yd.  long  and  the  other  2J  yd.  long,  how 
many  yards  of  ribbon  does  she  buy  ? 

We  see  that  we  must  add  4|  yd.  and  2|  yd. 

We  first  add  the  thirds,  thus : 

2._l2.  =  4=11 
3^3         3         -^3- 

We  write  the  ^  in  the  fractions'  column  and 
add  the  1  to  the  ones'  column.    Then  1  +  2  +  4  =  7,  and 
we  write  the  7  in  the  ones'  column. 

The  sum  is  7J,  and  so  Kate  buys  7J  yd.  of  ribbon. 

WRITTEN   EXERCISE 

1.  Nora  has  three  pieces  of  ribbon.  The  first  is  21  yd. 
long,  the  second  IJyd.  long,  and  the  third  41  yd.  long. 
How  many  yards  has  she  in  all  ? 

2.  Fred  is  making  a  picture  frame  that  is  91  in.  high  and 
7^ in.  wide.    How  many  inches  of  molding  does  he  need? 


Add 

the  following : 

3. 

4. 

5. 

6. 

7. 

8. 

H 

^ 

24J 

12f 

16f 

281 

^ 

^ 

161 

3f 

14| 

14| 

4 

6i 

17f 

^ 

15| 

15J 

9. 

10. 

11. 

12. 

13. 

14. 

2* 

li 

621 

391 

37J 

571 

3i 

7 

171 

12i 

291 

22| 

2 

H 

12 

331 

16 

33f 

ADDITION  AND  SUBTRACTION  203 

Subtracting  Fractions.    Sue  has  12  yd.  of  cloth.    She  uses 
2 J  yd.  for  a  doll's  suit.    How  many  yards  has  she  left? 

We  must  subtract  2f  yd.  from  12  yd. 

We  cannot  take  |-  from  nothing,  so  we  think 
of  12  as  llf ,  which  we  can  do  because  f  =  1. 

We  see  that  f  —  f  =  J,  aud  we  write  the  ^  in 
the  fractions'  column.  Then  11  —  2  =  9,  and  we 
write  the  9  in  the  ones'  column. 

The  difference  is  9J,  and  so  Sue  has  91  yd.  left. 

WRITTEN  EXERCISE 

1.  If  you  have  a  piece  of  paper  121  in.  long,  and  cut  off 
a  piece  3f  in.  long,  how  long  is  the  piece  that  is  left  ? 

Why  does  12^  —  3§  have  the  same  result  as  11 J  —  3§  ? 

2.  If  James  saws  a  piece  of  board  8 J  in.  long  from  a 
piece  24  in.  long,  how  long  is  the  piece  that  is  left  ? 


Subtract  the 

following : 

3. 

4. 

5. 

6. 

7. 

8. 

8 

6 

9 

7 

18 

36 

H 

^1 
^2 

^ 

2f 

H 

18f 

9: 

10. 

11. 

12. 

13. 

14. 

^ 

H 

^ 

^ 

161 

481 

4,i 

2J 

21 

3| 

8f 

36f 

15. 

16. 

17. 

18. 

19. 

20. 

9f 

9f 

n 

8i 

15i 

361 

2i 

2i 

2| 

If 

2i 

22| 

204  FRACTIONS 

WRITTEN  EXERCISE 

Add  and  also  subtract,  thus  'making  two  examples  in  each 
case.    Time  yourself. 

1.  2.  3.  4.  5. 

147f      1471      628|      4081     .  3601 
291       29f      342|     '  2991      1961 


6. 

7. 

8. 

9. 

10. 

4201 

342 

4271 

3261 

5801 

168 

1991 

■  129f 

1291 

•   268| 

11. 

12. 

13. 

14. 

15. 

600f 

5091 

4031 

6801 

9591 

1291 

268| 

227| 

273 

5481 

16. 

17. 

18. 

19. 

20. 

9001 

700 

600 

800 

7111 

5481 

2751 

296i 

127f 

122| 

21. 

22. 

23. 

24. 

25. 

401J 

3001 

911 

801 

820f 

67| 

48| 

991 

27i 

444J 

26. 

27. 

28. 

29. 

30. 

9561 

808| 

747f 

827| 

7201 

5191 

2441 

2451 

649^ 

278| 

31. 

32. 

33. 

34. 

35. 

6011 

7221 

800 

741J 

655| 

326 

644| 

235i 

362i 

4671 

FEACTIONAL  PARTS  205 

ORAL  EXERCISE 

1.  One  half  equals  how  many  fourths  ? 

2.  How  many  small  squares  in  J  of  the  large  square  ? 

3.  How  many  small  squares  in  the  large  square  ?  How 
many  fourths  make  1  ? 

4.  There  are  4  qt.  in  a  gallon.    What  name 
do  we  give  to  a  quarter  of  a  gallon  ? 

5.  Read  and  learn :  f  =  f;  i  +  f  =  l;  f  =  l 

6.  By  what  number  do  we  divide  to  find  one  fourth  of 
any  number  ? 

7.  How  many  fifths  of  the  circle  in  the  circle?    We 
have  seen  that  we  write  one  fifth  thus :  J. 

8.  Read :  J-  and  ^  are  |-. 

9.  How  much  is  J^  of  the  circle  and  ^ 
of  the  circle  ? 

10.  Read  and  learn :  |^  +  J  =  1;  f  =  l. 

11.  By  what  number  do  we  divide  to  find  one  fifth  of 
any  number  ?  to  find  one  eighth  of  any  number  ? 

12.  Think  one  fourth  of  each  of  these  numbers  and  then 
state  f  of  each :  8,  16,  20,  24,  12,  40,  28. 

13.  Think  one  fifth  of  each  of  these  numbers  and  then 
state  f  of  each :  25,  15,  30,  20,  40,  50,  55. 

14.  Think  one  sixth  of  each  of  these  numbers  and  then 
state  f  of  each :  12,  24,  18,  30,  48,  36,  54,  60,  66. 

15.  Think  one  eighth  of  each  of  these  numbers  and  then 
state  I  of  each :  16,  24,  40,  56,  80,  48,  32,  64,  88. 


206  FRACTIONS 

ORAL  EXERCISE 

1.  Write  these  columns  on  the  board,  and  add : 
3758469        10       20 
3758469        10        20 
3        7        5        8        4        6        9        10       20 
3758469        10       20 

2.  How  much  is  J  of  12?  J  of  12?  f  of  12? 

3.  How  much  is  1  of  28  ?  1  of  28  ?  f  of  28  ? 

4.  How  much  is  i  of  20?  1  of  20?  |  of  20? 

5.  State  the  values  of : 


lof  32 

lof  16 

iof24 

lof  36 

lof  40 

Jof  32 

iof  16 

iof  24 

lof  36 

fof  40 

f  of  32 

|of  16 

J  of  24 

fof  36 

fof  80 

6.  At  32^  a  yard,  what  will  f  of  a  yard  of  cloth  cost? 

7.  At  28^  a  pound,  what  will  ^  of  a  pound  of  meat  cost  ? 

8.  At  36^  a  dozen,  what  will  J  of  a  dozen  eggs  cost? 

WRITTEN  EXERCISE 

1.  Build  columns  of  four  12's  and  four  15's,  and  add. 

Copy  and  complete  the  followinrj  : 

2.  1  of  48  =              5.  i  of  44  =  8.  J  of  80  = 

3.  lof  48=              6.  Jof44=  9.  lof  80^ 

4.  fof  48=             7.  lof  40=  10.  fof  88  = 

-    11.  To  find  J  of  a  number  we  divide  the  number  by  4, 
How  much  is  J  of  400  ?  i  of  500  ?  J  of  600  ? 


FRACTIONAL  PARTS  20T 


ORAL 

EXERCISE 

State  the  values  of: 

1.  1  doz. 

\  doz. 

idoz. 

^  doz. 

J^doz. 

2.  f  doz. 

f  doz. 

f  doz.  ' 

3-^2  doz. 

^  doz. 

3.  There  being  36  inches 

\  in  1  yard, 

state  the  values  of  : 

*yd- 

J  yd. 

iyd. 

iyd. 

Jyd- 

State  the  values  of: 

4.  1  of  4 

1  of  10 

lof  12 

lof  20 

lof  16 

5.  1  of  4 

iof  12 

lof  16 

lof  24 

lof  36 

6.  1  of  5 

Jof  20 

lof  15 

lof  30 

lof  50 

7.  1  of  6 

lof  15 

lof  21 

lof  12 

lof  18 

8.  ^  of  8 

lof  16 

lof  32 

lof  40 

lof  80 

WRITTEN  EXERCISE 

Write  the  values  of: 


1. 

lof  18 

fof  18 

lof  21 

fof  21 

fof  30 

2. 

iof  16 

|of  16 

i  of  32 

fof  32 

fof  40 

3. 

lof  25 

fof  25 

fof  25 

f  of  50 

fof  50 

4. 

lof  12 

fof  12 

lof  18 

f-  of  18 

iof  60 

5. 

lof  16 

fof  16 

1  of  16 

iof  80 

fof  80 

6.  We  know  that  2  is  f  of  6,  that  3  is  J  of  9,  and  so  on. 
Write  five  numbers  that  equal  f  of  other  numbers. 

7.  Write  five  numbers  each  of  which  is  equal  to 

i  of  some  other  number  f  of  some  other  number 

J  of  some  other  number  f  of  some  other  number 


208  FRACTIONS 

WRITTEN  EXERCISE 

Find  the  following  parts  of  the  numbers  given: 

1.  1  of  126,  I  of  126.  13.  i  of  225,  f  of  225. 

2.  1  of  330,  f  of  330.  14.  3  of  225,  f  of  225. 

3.  J  of  450,  f  of  450.  15.  J,of  335,  f  of  335. 

4.  1  of  510,  f  of  510.  16.  f  of  725,  f  of  865. 

5.  1  of  639,  f  of  639.  17.  i  of  336,  f  of  336. 

6.  i  of  723,  f  of  723.  18.  i  of  726,  f  of  726. 

7.  1  of  128,  I  of  128.  19.  |  of  328,  f  of  328. 

8.  i  of  224,  f  of  224.  20.  f  of  328,  |  of  328. 

9.  i  of  328,  I  of  328.  21.  |  of  480,  f  of  488. 

10.  1  of  344,  f  of  344.      22.  i  of  147,  f  of  847. 

11.  1  of  524,  f  of  524.     23.  f  of  287,  f  of  294. 

12.  i  of  672, 1  of  672.      24.  f  of  810,  f  of  720. 

25.  How  do  you  find  J  of  a  number  ?   How  do  you  find 
f  of  150?  f  of  75?  I  of  300? 

26.  Frank  has  65  marbles  and  Rob  has  f  as  many. 
How  many  marbles  has  Rob? 

27.  K  45  drops  of  water  make  a  teaspoonful,  how  many 
drops  of  water  make  |-  of  a  teaspoonful  ? 

28.  Mary  uses  10  yd.  of  cloth  in  making  a  dress,  and 
Kate  uses  J  as  much.    How  much  does  Kate  use  ? 

V  29.  Fred  has  a  kite  string  that  is  328  ft.  long,  and  Will 
has  one  that  is  -J  as  long.  How  long  is  Will's  kite  string  ? 
\  30.  A  man  has  $720  in  the  bank  and  draws  out  f  of  it. 
How  much  does  he  draw  out  ?  How  much  is  left  ? 


ADDITION  AND  SUBTRACTION 


209 


ORAL  EXERCISE 

1.  Calling   the  large  rectangle  one,  how  many  halves 
do  you  see  in  1? 

2.  How    many    fourths 
do  you  see  in  i-  ?   in  1  ? 

3.  How    many    eighths 
do  you  see  in  J?  in  J?  inl? 

4.  How   many   sixths   do   you 


i 

i 

see  in  ^?   in  1?  i       i i__i i i i 

5.  1^  =  how  many  sixths  ?  i 1 1 1 

6.  How  many  sixths  do  you  see  in  ^  ?   in  -|  ?   in  |-  ? 

7.  If  we  have  a  piece  of  ribbon  l  yd.  long  and  another 
piece  J  yd.  long,  have  we  enough  for  trimming  a  doll's  dress 
that  needs  a  piece  f  yd.  long  ? 

We  see  by  the  rectangles  above  that  J  = 
and  so  I  +  J  =  I  +  J. 

But  just  as  2^  + 1^  =  3^,  so  J  +  J  =  f. 

So   the   sum   is   f,   and  we   have  enough 
trimming  for  the  doll's  dress. 

In.  these  simple  examples  for  beginners  we  need  not  consider  the  ques- 
tion of  loss  in  sewing  the  two  pieces  together. 

Looking  at  the  above  figures,  add  or  subtract  as  stated : 


=  2 
4' 


1=2. 
2         4 

1  =  1 
4         4 

3 

4 


8. 

9. 

10. 

11. 

12. 

i  +  i 

i  +  i 

f-i 

i  +  i 

1-i 

1—1 

2         4 

i-i 

7  _  1 
■g"        1" 

1  _  1 

2  8 

1-i 

3  _  1 

4  2 

i  +  i 

l-l 

i-i 

1-J 

i  +  1 

4^2 

i-i 

3  _  5_ 

4  8 

f-i 

1-i 

210  FRACTIONS 

ORAL  EXERCISE 

1.  Express  ^  as  eighths.    To  the  result  add  f . 

2.  If  you  are  making  a  bird  house  and  fasten  a  strip  of 
molding  ^  in.  thick  to  a  strip  of  wood  J  in.  thick,  how 
thick  are  the  two  together  ? 

3.  Express  f  as  eighths.    To  the  result  add  ^. 

4.  If  we  sew  together  insertion  ^  in.  wide  and  lace  ^  in. 
wide,  how  wide  are  the  two  ? 

5.  Express  J  as  eighths.    To  the  result  add  J. 

6.  If  you  lay  a  notebook  1  in.  thick  on  a  book  ^  in. 
thick,  how  thick  are  the  two  together  ? 

7.  How  do  you  add  two  fractions  ? 

WRITTEN   EXERCISE 

Add  the  following : 
111  611^  11    J S 5_ 

*■'    2'   2*  "•    6'   6>   6-  *-^'  12?   12'   12" 

2      111  7     JL      3  19        3         3         7 

*•    3'   3'   3*  '•    10'  nr*  **•  16'   16'   16- 

qlll  Q113  1Q357 

•»•    t'  4'  t'  °-    8'   8'  ¥'  ^^'  16"'  T6'  re- 

4II2  Q15.3  14       1         3         5 

*•    5'    S^'  H'  ^'     8'    8'  "g^-  *-^'  16'    16'    16- 

»»     1    1     2.  10       1        3      _7  IK        5         5         7 

''•    4'  4'  4-  •^""    rO"'  rO"'  in-  •^''*  16'    16'   16- 

Add,  as  explained  in  the  oral  exercise  on  page  205 : 

16.  1,1  20.  if  24.  If.  28.  11  +  1 

17.  1,J.  21.  If  25.  l,f  29.   21  +  1 

18.  1  f  22.  1  f  26.  I,  f  30.  71  +  Sf 

19.  If  23.  If  27.  I,  f  31.  5l  +  2f. 

It  is  not  expected  that  pupils  will  be  able  to  reduce  the  results  to  lowest 
terms  at  this  time. 


ADDITION"  211 

WRITTEN  EXERCISE 

1.  If  we  have  21  yd.  of  cloth  in  one  piece  and  IJyd. 
in  another,  how  much  have  we  in  both? 

2.  If  we  buy  1^  yd.  of  one  kind  of  ribbon  and  f  yd.  of 
another  kind,  how  much  do  we  buy  in  all? 

Add  the  following: 


3. 

31  4-1 

8. 

Ql  _1_  3 

0^  +  4. 

13. 

3f4-|. 

4. 

3f  +  2i. 

9. 

7|-  +  9|-. 

14. 

6|  4-  7|. 

5. 

^+h 

10. 

21  4-  31 

15. 

31  4-  2-f . 

6. 

31  4-  21. 

11. 

3|  4-  21. 

16. 

9|  +  6i. 

7. 

4|  +  6f . 

12. 

3J  +  51. 

17. 

4f  4-  &l 

18.  If  a  desk  is  21  ft.  long  and  IJ  ft.  wide,  what  is  the 
sum  of  the  length  and  width  of  the  desk  ? 

Add  the  following : 

19.  21  4-  11  25.  21  + 11.  31.  41  4-  IJ 

20.  31  +  51  26.  41 +  61  32.  51  +  71 

21.  8|  +  5.  27.  6|-  +  8i.  33.  3J  +  5f 


25. 

21  + If 

26. 

41  +  6J. 

27. 

6f  +  SJ. 

28. 

7f  +  2f . 

29. 

H  +  5f  • 

30. 

3|  +  81 

22.  4|  +  63^.               28.  7|  +  2|.  34.  6f  +  71 

23.  9f  +  2f .                  29.  61  +  5J.  35.  7-1  +  If 

24.  5i  +  2lf                30.  3|  +  8l  36.  2 J  +  5f 

37.  If  you  place  a  board  |  in.  thick  on  a  plank  that  is 
If  in.  thick,  what  is  the  total  thickness  ? 

38.  If  you  place  a  plank  1^  in.  thick  on  a  beam  that  is 
8 J  in.  thick,  what  is  the  total  thickness  ? 


212  FRACTIONS 

Subtraction.  1.  In  making  a  picture  frame  Louis  cut  a 
piece  of  molding  5|-  in.  long  from  a  piece  8 J  in.  long.  How 
long  was  the  piece  that  was  left  ? 

We  see  that  8|  -  5|  =  3|. 

We  know  from  the  pictures  on  page  209  that  f  =  J,  and 
so  3f  =  3J.   That  is,  Louis  has  3 J  in. 'of  molding  left. 

2.  How  much  picture  molding  will  Louis  have  left  if 
he  takes  2|  in.  from  8  in.  ? 

We  know  that  8  =  7f ,  because  f  =  1- 

We  see  that  7|  —  2^  =  5J,  and  so  Louis  has  5J  in.  left. 

3.  How  much  picture  molding  will  Louis  have  left  if 
he  takes  2 J  in.  from  8J  in.  ? 

We  see  that  f  is  greater  than  J,  and 
so  we  cannot  take  f  from  ^. 
We  see  that  ^=^  +  ^  =  7|. 
We  know  that  J  =  f  • 
So  we  can  take  2J  from  7f . 
The  answer  is  5f ,  and  so  Louis  has  5f  in.  left. 


WRITTEN  EXERCISE 

1.  If  from  10  yd.  of  cloth  we  cut  21  yd.,  how  much  cloth 
is  left? 

2.  If  from  15  yd.  of  ribbon  we  cut  5|  yd.  and  IJ  yd., 
how  much  ribbon  is  left  ? 


8*  = 

H 

=  7f 

2|  = 

2| 

=  2f 
5f 

Subtract  the  following : 

3.5i-l       5.5-14. 

7.  2-f. 

9-  7J-5i 

4.  7|-J.       6.  7-3J. 

8.  51 -3J. 

10.  8J-4J 

MEASURES  213 


VIII.   MEASURES 
ORAL  EXERCISE 

1.  How  many  pints  are  there  in  a  quart? 

2.  A  pint  is  what  part  of  a  quart  ? 


Liquid  Measure.  The  table  of  Hquid  measure  is  as  follows ; 
4  gills  (gi.)  =  1  pint  (pt.) 
2  pints  =  1  quart  (qt.) 
4  quarts  =  1  gallon  (gal.) 

Express  the  following  as  pints: 

3.  2qt.  5.  5qt.  7.  7  qt. 

4.  11  qt.  6.  Iqt.  8.   IJ  qt. 

Express  the  following  as  quarts : 

11.  2pt.  13.  4pt.  15.  8pt. 

12.  20  pt.  14.  Igal.  16.  2  gal. 

Illustrative  Problems.    1.  Express  7  qt.  as  pints. 
Since  1  qt.  =  2  pt., 

therefore  7  qt.  =  7  x  2  pt.,  or  14  pt. 

2.  Express  36  qt.  as  gallons. 
Since  1  qt.  =  J  gal., 

therefore  36  qt.  =  36  x  l  gal.,  or  9  gal. 

Pupils  at  this  stage  of  their  work  are  not  expected  to  explain  such 
reductions  very  elaborately.  The  above  forms  are  accurate,  but  a  pupil 
might  properly  think,  for  example,  that  there  are  4  qt.  in  1  gal.,  and  in 
36  qt.  there  are  as  many  gallons  as  36  -^  4,  or  9  gal. 


9. 

10  qt. 

10. 

21  qt. 

17. 

10  pt. 

18. 

4  gal. 

214  MEASURES 

WRITTEN  EXERCISE 

Express  the  following  as  quarts: 

1.  75  gal.  3.  48  pt.  5.  175  gal.  7.  J  gal. 

2.  145  gal.         4.  98  pt.  6.  180  pt.  8.  11  gal. 

Exjoress  thefolloioing  as  gallons: 

9.  8qt.  11.  96  qt.        13.  168  qt.  15.  240  qt. 

10.  36  qt.  12.  96  pt.        14.  168  pt.  16.  240  pt. 

17.  If  Martha's  mother  buys  2  qt.  of  milk  to-day  and 
pays  8^  a  quart,  how  much  does  the  milk  cost  ?  How  much 
is  she  paying  for  each  pint  of  milk  that  she  buys  ?  How 
much  would  a  gallon  of  milk  cost? 

18.  If  Mr.  Lane,  the  grocer,  buys  60  gal.  of  vinegar,  and 
puts  it  up  in  quart  bottles  for  sale,  how  many  quart  bottles 
can  he  fill  ?   How  many  pint  bottles  could  he  fill  ? 

19.  If  the  milkman  charges  30  (^  a  pint  for  cream,  how 
much  does  he  charge  a  quart  ?  If  he  has  a  gallon  of  cream 
and  sells  it  all,  how  much  does  he  get  for  it  ? 

20.  If  mother  buys  a  gallon  of  molasses  and  uses  a  pint 
each  day  in  cooking,  how  long  will  the  molasses  last  ? 

21.  How  many  pint  bottles  can  a  dealer  fill  from  75  qt. 
of  milk  ? 

Oral  and  written  work  of  this  kind  should  be  given  to  show  the  relations 
of  the  parts  of  each  table,  one  to  another.  This  textbook  furnishes  plenty 
of  such  abstract  work,  but  the  teacher  may  profitably  supplement  it  by 
home  problems  made  by  the  class  and  representing  prices  in  the  community. 

There  should  also  be  given  simple  exercises  in  estimating  the  capacity 
of  boxes,  glasses,  pitchers,  and  the  like,  in  the  schoolroom. 


TIME  MEASURE  215 

Time  Measure.    The  table  of  time  is  as  follows : 

60  seconds  (sec.)  =  1  minute  (min.) 
60  minutes  =  1  hour  (hr.) 
24  hours  =  1  day  (da.) 
7  days  =  1  week  (wk.) 
About  4  weeks  =  1  month  (mo.) 
12  months  =  1  year  (yr.) 
100  years  =  1  century 

The  days  of  the  week  are  Sunday,  Monday,  Tuesday, 
Wednesday,  Thursday,  Friday,  Saturday. 

The  months  of  the  year  and  the  number  of  days  in  each 
month  are  as  follows  : 

January,  31  da.  July,  31  da. 

February,  28  or  29  da.  August,  31  da. 

March,  31  da.  September,  30  da. 

April,  30  da.  October,  31  da. 

May,  31  da.  November,  30  da. 

June,  30  da.  December,  31  da. 

Thirty  days  has  September, 

April,  June,  and  November. 

February  has  28  days  except  in  a  leap  year,  when  it  has 
29  days.  Until  the  year  2100,  every  fourth  year  is  a  leap 
year;  that  is,  1916,  1920,  1924,  and  so  on,  are  leap  years. 
Ordinary  years  have  365  days ;  leap  years  have  366  days. 
There  are  52  weeks  and  1  day  in  an  ordinary  year. 

Every  morning  the  teacher  should  have  some  of  the  pupils  write  on  the 
blackboard  the  day  of  the  week  and  the  day  of  the  month. 


216  MEASUEES 

ORAL  EXERCISE 

1.  What  month  is  this ?   What  was  last  month? 

2.  What  is  next  month  ?  the  month  after  that  ? 
.  3.  Name  the  months  of  the  year. 

4.  Name  the  days  of  the  week.    What  day  is  this  ? 

5.  What  months  have  thirty  days  ? 

6.  How  many  days  are  there  in  this  month  ? 

7.  What  day  of  the  month  is  this  ? 

8.  On  what  days  of  the  week  do  you  go  to  school  ? 

The  pupil  should  be  taught  to  understand  the  calendar,  and  the  calendar 
for  the  mouth  should  be  hung  in  the  schoolroom. 

WRITTEN  EXERCISE 

1.  How  many  days  are  5  da.  +  2  da.?   How  many  weeks 
do  they  make  ? 

2.  How  many  days  are  7  da.  +  7  da.?   How  many  weeks 
do  they  make  ? 

3.  How  many  weeks  are  7  da.  +  7  da.  +  7  da.  ?  How  many 
days  in  2  wk.?  in  3  wk.? 

4.  How  many   seconds   are   2  x  30  sec?    How  many 
minutes  in  60  sec?  in  120  sec? 

5.  How  many  seconds  are  40  sec  +  20  sec.  ?  How  many 
minutes?   How  many  minutes  in  360  sec? 

6.  How  many  seconds  are  60  sec.  4-  60  sec.  ?  How  many 
minutes?   How  many  minutes  in  600  sec? 

7.  How  many  more  days  in  January  than  in  February 
of  this  year? 


MEASUEES  217 

PROBLEMS  WITHOUT  NUMBERS 

1.  How  do  you  multiply  by  a  number  of  two  figures, 
the  right-hand  figure  being  zero  ? 

2.  How  do  you  multiply  a  number  representing  dollars 
and  cents  by  a  number  ending  in  zero  ? 

3.  How  do  you  divide  a  number  ending  in  zero  by  a 
two-figure  number  ending  in  zero? 

4.  If  a  division  is  exact,  the  dividend  is  the  product  of 
what  two  numbers  ? 

5.  How  do  you  check  the  work  in  exact  division  ? 

6.  How  do  you  find  a  fourth  of  any  number  ?   How  do 
you  find  three-fourths  of  the  number  ? 

7.  How  do  you  find  three-fifths  of  any  number  ? 

8.  How  do  you  add  fourths  and  eighths  ?  fourths  and 
halves  ?  halves  and  eighths  ? 

9.  If  you  know  how  many  quarts  a  can  will  hold,  how 
do  you  find  the  number  of  pints  ? 

10.  If  you  know  the  number  of  gallons  a  pail  will  hold, 
how  do  you  find  the  number  of  quarts  ? 

11.  How  do  you  change   pints  to  quarts?    quarts   to 
gallons  ? 

12.  How  would  you  find  the  number  of  seconds  in  an 
hour  ?  the  number  of  hours  in  a  week  ? 

13.  How  would  you  find  the  number  of  minutes  in  a 
day?  in  a  week?  in  a  year? 

14.  If  you  know  the  cost  of  milk  by  the  quart,  how  do 
you  find  the  cost  by  the  gallon  ? 


218  EEVIEW 

IX.   EEVIEW 
WRITTEN  REVIEW 

1.  A  fruit  train  of  19  cars  was  loaded  with  oranges.  If 
there  were  324  boxes  in  each  car,  how  many  boxes  were 
in  the  whole  train? 

2.  A  bushel  of  corn  weighs  56  lb.  How  many  bushels 
are  there  in  1792  lb.  of  corn  ? 

3.  A  dealer  sold  28  building  lots  at  an  average  price 
of  $366.   How  much  did  he  receive  for  the  lots? 

4.  If  27  typewriters  cost  a  dealer  $1701,  how  much 
does  the  dealer  pay  for  each  typewriter? 

5.  If  a  man  spends  $48  a  year  for  cigars,  how  much 
will  he  spend  for  cigars  in  25  yr.  ? 

6.  A  farmer  raised  4212  bu.  of  corn  on  78  acres.  How 
many  bushels  did  he  raise  per  acre  ? 

7.  If  a  man  earns  $3.20  a  day,  how  much  will  he  earn 
in  28  da.  ? 

8.  How  many  square  feet  are  there  in  a  lot  120  ft. 
long  and  58  ft.  wide  ? 

9.  How  many  steel  rails  each  33  ft.  long  will  be  re- 
quired for  5940  ft.  of  track?  Remember  that  a  track 
has  two  lines  of  rails. 

10.  In  an  orchard  containing  1440  trees  there  are  45 
rows  of  trees.    How  many  trees  are  there  in  a  row? 

11.  A  man  saved,  $1260  in  28  months.     How  many 
dollars  did  he  save  a  month? 


WRITTEN  REVIEW 

219 

WRITTEN  REVIEW 

Add  the  following 

1.                   2. 

3. 

4. 

5. 

2473             2975 

$2.75 

$12.82 

$25.85 

4826             8372 

3.86 

4.96 

17.68 

6.                   7. 

8. 

9. 

10. 

3426             5383 

$4.75 

$32.75 

$53.42 

4289             2468 

2.68 

18.26 

26.89 

2976             9289 

3.42 

4.98 

14.93 

Suhtraxit  the  following : 

11.                  12. 

13. 

14. 

15. 

4012             9235 

$7.61 

$11.72 

$91.26 

3746             6842 

2.95 

6.85 

13.41 

Multiply  or  divide 

as  'indicated : 

16.  17  X  $2.75. 

21.  14,620 -J 

-  37.          26. 

228 

x228. 

17.  23  X  $1.86. 

22.  42,836^ 

-  74.          27. 

346 

x482. 

18.  48  X  $12.62. 

23.  53,000^ 

-  75.          28. 

527 

x693. 

19.  56  X  $27.35. 

24.  48,125 -f 

-  25.          29. 

648 

x987. 

20.  74  X  $68.75. 

25.  81,348^ 

-  46.          30. 

209 

x209. 

Find  the  answers  to  the  following  : 

31.  f  of  162.            34.  f  of  275.  37.  16  qt.  =  (?)  pt. ' 

32.  J  of  168.            35.  I  of  176.  38.  16  gal.  =  (?)  qt. 

33.  f  of  225.            36.  f  of  352.  39.  28  da.  =  (?)  wk. 


220  USING  WHAT  YOU  HAVE  LEARNED 

X.   USING  WHAT  YOU  HAVE  LEARNED 
TAKING  A  TRIP 

1.  Arthur's  father  took  him  on  a  trip  from  Indianapolis 
to  Chicago.    They  left  at  half  past  eleven  in  the  morning 


and  arrived  at  five  in  the  afternoon.   How  long  were  they 
in  taking  the  trip  ? 

2.  It  is  109J-  miles  from  Cincinnati  to  Indianapohs,  and 
3031  miles  from  Cincinnati  to  Chicago.  How  far  is  it  on 
the  trip  that  Arthur  and  his  father  took  to  Chicago  ? 

3.  If  the  railroad  charged  for  195  miles,  at  2(^  a  mile, 
how  much  did  Arthur's  father  pay  for  a  ticket  for  himself  ? 

4.  They  bought,  for  luncheon  on  the  train,  8  sandwiches 
at  10^  each,  6  cookies  at  10^  a  dozen,  and  4  oranges  at  5^ 
each.   How  much  did  the  luncheon  cost  ? 

6.  They  left  Chicago  at  15  min.  before  one  and  reache(qt 
Indianapolis  at  6  o'clock.    How  long  did  this  take  ? 


PROBLEMS  221 

6.  Arthur  and  his  father  saw  these  prices  at  the  lunch 
counter  in  the  station  : 


Sandwiches, 

10^ 

Cookies, 

3(^ 

Coffee, 

10(^ 

Oranges, 

6(^ 

Milk, 

10.)^ 

Bananas,  . 

H 

Oatmeal, 

20  (^ 

Apples, 

3(^ 

Bread  and  milk. 

15^ 

Pies, 

10(^ 

Cold  ham. 

25(^ 

Soup, 

20^ 

Cold  beef. 

25^ 

Ice  Cream, 

20  (^ 

From  this  list  select  five  things  that  you  would  like  to 
eat  for  luncheon,  and  find  the  cost. 

7.  If  Arthur's  father  took  2  sandwiches,  a  cup  of  coffee, 
some  cold  beef,  and  an  orange,  what  did  his  luncheon  cost  ? 

Use  the  above  list  in  Exs.  7,  8,  and  9. 

8.  If  Arthur  took  a  sandwich,  a  glass  of  milk,  a  piece  of 
pie,  and  2  cookies,  how  much  did  his  luncheon  cost  ? 

9.  A  man  sat  beside  Arthur  and  ordered  some  oatmeal, 
a  cup  of  coffee,  some  cold  ham,  and  2  bananas.  How  much 
did  his  luncheon  cost  ? 

10.  If  Arthm-'s  father  paid  75^  for  a  drive  in  a  taxi,  $1 
for  two  rides  in  a  bus,  and  50  ^  for  delivering  a  trunk  which 
he  brought  home,  how  much  did  he  pay  for  all  ? 

11.  Find  the  cost  of  a  trip  on  which  a  man  paid  the 
following:  ticket,  $2.70;  baggage,  50^;  luncheon,  65 (j^. 

12.  Find  the  cost  of  a  trip  on  which  a  man  paid  the 
following:  ticket,  $7.60;  sleeper,  $1.75;  dining  car,  $1.25; 
porter,  25(^;  taxi,  $1.25;  hotel  bill,  $12.50. 


222  LITTLE  EXAMINATIONS 

XI.   LITTLE  EXAMINATIONS 

I.  1.  578  +  296.  5.  428  x  324.      9.  2568  ^  321. 

2.  $2.75 +  $3.69.  6.509x672.  10.  J  ft.  =  (?)  in. 

3.  342-196.    7.  7344^36.  11.  60  gal.  =  (?)qt. 

4.  24  X  86.      8.  XC  =  (?).  •  12.  i  of  729. 

11.  1.  983  +  432.    5.  286  x  981.   9.  2830  -  283. 

2.  $4.87  +  $3.73.  6.  870  x  392.  10.  1200  ft.  =  (?)  yd. 

3.  481-296.    7.  5304^26.  11.  60  qt.=  (?)gal. 
4.48x94;      8.  LXXI  =  (?).  12.  i  +  J  +  i 

TIL  1.  887  +  556.    5.  534  x  787.   9.  6084  h-  432. 

2.  $2.88  +  $1.97.  6.  508  x  667.  10.  888  ft.  =  (?)  yd. 

3.  513  -  234.    7.  3968  h-  31.  11.  40  pt.  =  (?)  qt. 
4.33x69.      8.  XLI  =  (?).  12.  i  +  J. 

IV.  1.  789  +  987.    6.  609  x  770.  11.  240  min.  =  (?)sec. 

2.  $4.47  +  $2.89.  7.  6952  ^  44.  12.  40  qt.  =  (?)  pt. 

3.  812  -  296.    8.  LXIV  =  (?).  13.  1  -  f . 

4.  77  X  98.      9.  4500  -^  375.  14.  J  of  352. 

5.  642  X  889.    10.  360  x  430.  15.  6087-  45. 
V.  1.  276  +  688.    6.  783  x  892.  11.  8536  -^  194. 

2.  $3.39 +  $2.47.  7.  340  x  820.  12.  240sec.  =  (?)mm. 

3.  723  -  465.    8.  6336  ^  48.  13.  4  lb.  =  (?)  oz. 

4.  64  X  39.      9.  XCI  =  (?).  14.  64  oz.  =  (?)  lb. 

5.  680  X  732.    10.  CIX  =  (?).  15.  300  x  5280. 

Teachers  should  read  the  note  on  page  52. 


CHAPTER  V 

I.  EEADING  AND  WRITING  NUMBERS 
ORAL  EXERCISE        ^ 

1.  Name  the  places   from   right   to  left  as  you  have 
learned  them  in  writing  a  number  of  five  figures. 

2.  What  is  the  smallest  number  and  the  largest  number 
that  can  be  written  with  five  figures  ? 

3.  K  you  add  one  to  99,999,  what  is  the  sum  ? 

4.  Read  these  numbers : 

1,000    200,000    125,000    237,630 

10,000    300,000    275,000    342,275 

100,000    900,000    468,921    407,507 

WRITTEN  EXERCISE 

Write  in  figures : 

1.  Seventy-five  thousand,  sixteen. 

2.  Two  hundred  thousand,  four  hundred  six. 

3.  Five  hundred  fifty-five  thousand,  seven. 

4.  Nine  hundred  ninety-nine  thousand,  nine  hundred. 

Write  in  loords : 

5.  125,050.  7.  500,005.  9.  100,100. 

6.  304,004.  8.  101,010.  10.  123,456. 

223 


224  READING  AND  WRITING  NUMBERS 

Million.  There  is  a  special  name  for  a  thousand  thousand. 
This  number  is  called  a  million,  and  is  written  1,000,000. 

We  count  millions  just  as  we  count  thousands.  That  is, 
5,000,000  is  5  million,  273,000,000  is  273  million,  and 
170,050,270  is  170  million,  50  thousand,  270. 

For  easy  reading  we  separate  by  commas  the  figures  of 
a  large  number  into  groups  of  three,  always  beginning  at 
the  right,  thus  :  175,926,284.  All  these  groups  must  have 
three  figures,  except  the  left-hand  one ;  thus  : 

1,275,340  30,000,000  425,000,723 

21,426,580  120,000,000  196,481,278 

The  name  of  the  first  group  at  the  right  is  ones ;  of  the 
second  group,  thousands ;  of  the  third  group,  millions. 

ORAL  EXERCISE 

Read  these  large  numhers  : 

1.  1,253,429  28,276,390  126,289,000 

2.  2,426,000  43,070,001  342,428,476 

WRITTEN  EXERCISE 

Write  in  figures : 

1.  Sixteen  milhon,  two  thousand,  nine. 

2.  Seventy-one  million,  five  hundred  seventy. 

3.  Sixty-two  million,  four  thousand,  six. 

4.  Four  hundred  seventy-nine  million. 

5.  Five  hundred  fifteen  million,  three  hundred. 

6.  Six  million,  ninety-three  thousand,  seventeen. 


ADDITION  225 

II.   ADDITION 
ORAL  EXERCISE 

To  each  of  the  following  numbers  add  2,  3,  4, 5,  6,  7,  8, 
and  9,  in  turn : 

1.  27       26       45       74       33       52       21       96 

2.  82       83       38       62       17       15       34       61 

To  each  of  the  following  add  10, 11,  and  20,  in  turn : 

3.  4        12        49        24        14        23        16        21 

4.  7        20        13       38        19       27       66        90 

WRITTEN  EXERCISE 

1.  Indiana  contains  36,350  square  miles ;  Iowa  contains 
56,025  square  miles;  Illinois,  56,650  square  miles.  What  is 
the  combined  area  of  these  states  ? 

2.  A  farmer  sells  six  loads  of  hay.  The  first  weighs 
2430  1b.;  the  second,  2350  1b.;  the  third,  2160  1b.;  the 
fourth,  1960  1b.;  the  fifth,  21401b.;  the  sixth,  1860  1b. 
How  much  do  the  six  loads  weigh  together  ? 

Add  the  following  numbers : 

3.  4.  5.  6. 

$227.75  $476.68  $883.60  $342.98 

184.84  204.69  445.38  38.28 

68.09  30.84  268.84  194.45 

224.65  26.85  97.25  230.68 

80.75  342.68  684.06  49.95 


226  SUBTRACTION 

III.  SUBTRACTION 
ORAL  EXERCISE 

1.  State  rapidly  the  remainders : 

37  37  37  37  37  46  52 

_7  10  17  _8  18  18  22 

From  92  subtract  tlw  following  numbers : 

2.  10  20  40  52  62  4  7 

3.  12  22  42  53  64  14  27 

4.  Louise  spent  64^  for  Christmas  and  Clara  spent  32^. 
How  much  more  did  Louise  spend  than  Clara  ? 

5.  Grandfather  is  85  years  old  and  father  is  50  years  old. 
How  much  older  than  father  is  grandfather  ? 


WRITTEN 

EXERCISE 

Subtract  and  check : 

1. 

2. 

3. 

4. 

$994.83 

$607.64 

$813.80 

$970.50 

538.80 

249.89 

396.78 

448.68 

5. 

6. 

7. 

8. 

$765.08 

$376.30 

$940.60 

$880.60 

259.69 

267.95 

430.54 

479.95 

9. 

10. 

11. 

12. 

$972.58 

$896.20 

$878.69 

$890.25 

348.99 

798.43 

362.90 

86.09 

MULTIPLICATIOISr  227 

IV.   MULTIPLICATION 
ORAL  EXERCISE 

1.  Recite  the  multiplication  table  of  5's. 

2.  Recite  the  multiplication  table  of  6's. 

3.  Recite  the  multiplication  table  of  7's. 

4.  Recite  the  multiplication  table  of  8's. 
6.  Recite  the  multiplication  table  of  9's. 

6.  If  1  doz.  cans  of  soup  cost  $2,  what  will  42  doz. 
cans  cost  ?   What  will  50  doz.  cans  cost  ? 

7.  If  1  doz.  jars  of  meat  extract  cost  |8,  what  will 
30  doz.  jars  cost  ?   What  will  40  doz.  jars  cost  ? 

8.  If  1  doz.  cans  of  lobster  cost  |3,  what  will  22  doz. 
cans  cost  ?   What  will  33  doz.  cans  cost  ? 

WRITTEN  EXERCISE 

Multiply  the  following : 

1.  $243  by  22.  11.  $924  by  43.  21.  $723  by  64. 

2.  $315  by  73.  12.  $672  by  94.  22.  $825  by  35. 

3.  $465  by  54.  13.  $941  by  85.  23.  $732  by  45. 

4.  $572  by  25.  14.  $682  by  69.  24.  $417  by  53. 

5.  $485  by  62.  15.  $617  by  82.  25.  $525  by  64. 

6.  $564  by  47.  16.  $426  by  91.  26.  $812  by  14. 

7.  $259  by  57.  17.  $324  by  28.  27.  $476  by  42. 

8.  $538  by  38.  18.  $416  by  29.  28.  $385  by  74. 

9.  $467  by  59.  19.  $675  by  25.  29.  $416  by  46. 
10.  $635  by  92.  20.  $530  by  24.  30.  $625  by  62. 


228 


MULTIPLICATION 


Three-Figure  Multiplier.  Mr.  Greene  bought  three  farms, 
the  first  containing  120  acres ;  the  second,  116  acres ;  and 
the  third,  102  acres.  If  he  paid  $125  an  acre  for  all  the 
land,  how  much  did  each  farm  cost  him  ? 

We  see  that  we  must  find  three  products,  120  x  $125, 
116  X  $125,  and  102  x  $125. 

We  learned  on  pages  180  and  181  how  to  multiply  by 
three-figure  numbers.    Study  these  three  multiplications: 


$125 

$125 

$125 

120 

116 

102 

2500 

750 

250 

125 

125 

125 

$15000 

125 
$14500 

$12750 

We  see  that  the  first  farm  cost  $15,000;  the  second, 
$14,500 ;  and  the  third,  $12,750. 


WRITTEN  EXERCISE 

Multiply  the  following : 


1.  115  X  136. 

2.  225  X  475. 

3.  142  X  387. 

4.  268  X  491. 

5.  380  X  662. 

6.  132  X  390. 

7.  243  X  487. 


8.  161x296. 

9.  314  X  417. 

10.  180  X  672. 

11.  201  X  325. 

12.  208  X  362. 

13.  405  X  488. 

14.  507  X  983. 


15.  708  X  807. 

16.  263  X  482. 

17.  478  X  298. 

18.  309  X  286. 

19.  440  X  555. 

20.  908  X  687. 

21.  693  X  447. 


THREE-FIGURE  MULTIPLIER  229 

WRITTEN  EXERCISE 

Multiply  the  following : 

1.  131  X  427.  7.  362  x  648.  13.  375  x  702. 

2.  101  X  363.  8.  407  X  942.  14.  406  x  1475. 

3.  242  X  787.  9.  387  x  682.  15.  368  x  3209. 

4.  303  X  525.  10.  805  x  377.  16.  402  x  2008. 

5.  575  X  766.  11.  994  x  782.  17.  498  x  2007. 

6.  909  X  999.  12.  809  x  696.  18.  909  x  1009. 

19.  "What  will  225  acres  of  land  cost"  at  $125  an  acre? 

20.  A  man  buys  15  acres  of  land  at  |62.50  an  acre,  and 
125  acres  at  $87.50  an  acre.   What  does  all  the  land  cost? 


Find  the  cost  of  the  following : 

21.  121  locomotives  at  $9875  each. 

22.  216  passenger  cars  at  $3950  each. 

23.  162  yd.  of  Wilton  carpet  at  $1.65  a  yard. 

24.  272  yd.  of  silk  at  $1.15  a  yard;  at  $1.25  a  yard. 

25.  112  building  lots  at  $1375  each;  at  $1250  each. 

26.  135  automobiles  at  $2450  each ;  at  $1875  each. 

27.  102  farm  wagons  at  $87.50  each ;  at  $92.25  each. 

Multiply  the  following : 

28.  $28.75  by  100  ;  by  101 ;  by  106  ;  by  108  ;  by  109. 

29.  $43.50  by  200 ;  by  207 ;  by  208 ;  by  306  ;  by  309. 

30.  $67.56  by  400  ;  by  406  ;  by  409  ;  by  403  ;  by  405. 

31.  $29.30  by  500;  by  504;  by  507;  by  508  ;  by  509. 

32.  $35.25  by  600 ;  by  609 ;  by  807  ;  by  808 ;  by  987. 


*  230  DIVISION 

V.  DIVISION 

ORAL  EXERCISE 

1.  How  many  lO's  in  30?  in  100  ?  in  700?  in  1000? 

2.  How  many  20's  in  40  ?  in  400  ?  in  800  ?  in  2000  ? 

3.  How  many  lOO's  in  300  ?  in  700  ?  in  1000  ?  in  8000  ? 

4.  Divide  the  following : 

500-10       500-5-.50       500^100       500^500 


Divisors  Ending  in  Zeros.   To  divide  24,000,  24,357,  and 
25,357  by  2000,  we  proceed  as  follows : 

2j?j3fj?)240j3f  2^0j?)24^^J  2j?0}2OT_ 

12  1 2-357  1 01357 

That  is,  we  cancel  (cross  out)  the  zeros  at  the  right  of  the 
divisor  and  cancel  as  many  figures  at  the  right  of  the  divi- 
dend as  we  cancel  zeros  of  the  divisor,  writing  the  complete 
remainder  over  the  divisor. 

Canceling  three  figures  divides  by  1000,  and  because  we 
divide  the  rest  by  2,  we  really  have  divided  by  2000. 

WRITTEN  EXERCISE 

Divide  the  following: 

1.  6000  -5-  300.  6.  4000  -^  200. 

2.  6007  -  300.  7.  4009  ^  200. 

3.  6107  -  300.  8.  4109  -  200. 

4.  60,107  -^  300.  9.  102,107  ^  6000. 

5.  69,107  ^  300.  10.  147,111  h-  7000. 


THREE-FIGURE  DIVISOR 


231 


25 

501)12525 
1002 
2505 
2505 


Three-Figure  Divisor.  To  divide  12,525  by  501  we  write 
the  numbers  in  the  same  way  as  in  other  cases  of  division. 

Since   12  -^  5    is  a   little   more   than   2,    we   see   that 
1252  -^  501  is  also  more  than  2,  but  less 
than  3. 

Since  2  x  501  =  1002,  we  subtract,  and 
there  is  a  remainder  of  250  tens. 

Since  we  divided  1252  tens,  we  write 
the  2  in  the  quotient  over  the  tens. 

Bringing    down   the   next   figure   as 
usual,  we  have  2505. 

Since  2505  -5-  501  =  5,  we  write  the  5  as  the  next  figure. 

The  quotient  is  therefore  25. 

Check.    25  X  501  =  12,525. 

If  the  quotient  figure  is  taken  too  large,  the  partial  prod- 
uct will  he  greater  than  the  corresponding  part  of  the  dividend. 
In  this  case,  try  a  smaller  quotient  figure. 

If  the  quotient  figure  is  taken  too  small,  the  remainder  will 
he  greater  than  the  divisor.  In  this  case,  try  a  larger  quo- 
tient figure. 

WRITTEN  EXERCISE 

Divide  the  following : 

7.  7398^274. 

8.  3675  ^  525. 

9.  3552  -H  888. 

10.  1926^321. 

11.  3024^432. 

12.  7011  ^  171. 


1.  1284-^321. 

2.  5733^273. 

3.  1415  -  283. 

4.  8450  -^  325. 

5.  9683  H-  421. 

6.  9541 


375. 

219'. 
9174-^278. 
7896  ^  329. 


329. 


13.  2250 

14.  7446 
15. 
16. 

17.  8536-388. 
5136  -  642. 


18. 


232 


DIVISION" 


WRITTEN  EXERCISE 

Divide  the  following : 
1.  15,000^125. 


2.  29,000  H- 125. 

3.  17,250^125. 

4.  25,984^-116. 

5.  77,604^116. 

6.  86,229^201. 

7.  76,708-302. 

8.  50,470  -  245. 

9.  93,632^176. 

10.  87,143^211. 

11.  93,860  ^  247. 

12.  91,739-5-199. 

13.  85,158  -^  249. 

14.  87,648-^249. 

15.  87,318^231. 

16.  91,791  H- 217. 

17.  65,649-237. 

35.  If  98  machines  cost 
each  machine? 

36.  If  175  tons  of  hay  cost  $2975,  what  is 
the  hay  per  ton  ? 

37.  If  405  sewing  machines  cost  a  dealer 
much  did  he  pay  for  each  machine  ? 


18.  84,300 

19.  17,000 

20.  16,875 

21.  29,375 

22.  51,736 

23.  52,576 

24.  28,644 

25.  70,512 

26.  32,568 

27.  79,442 

28.  69,834 

29.  72,670 

30.  79,692 

31.  82,450 

32.  79,808 

33.  78,200 

34.  69,687 

,594,  what  is 


281. 
125. 
125. 
125. 
116. 
212. 
231. 
226. 
236. 
314. 
226. 
215. 
229. 
194. 
232. 
184. 
^267. 

the  cost  of 


the  cost  of 
,175,  how 


MEASURES  233 

VI.   MEASURES 
ORAL  EXERCISE 

1.  How  many  inches  in  1  ft.  ?   in  |-  ft.  ? 

2.  How  many  feet  in  1  yd.  ?   in  |-  yd.  ?   in  1 J  yd.  ? 

3.  There  is  a  measure  called  the  rod.  It  is  16|-  ft.  long. 
How  much  does  this  lack  of  being  20  ft.  ?  It  is  how  much 
more  than  15  ft.  ?       

Length.    The  following  is  the  table  of  length : 

12  inches  (in.)  =  1  foot  (ft.) 
3  feet  =  1  yard  (yd.) 
16|  feet  =  1  rod  (rd.) 
5280  feet  =  320  rods  =  1  mile  (mi.) 

The  teacher  should  assist  the  pupils  to  visualize  these  basal  units.  In 
cities  the  number  of  blocks  to  the  mile,  the  number  of  feet  or  rods  in  the 
width  of  the  streets,  and  the  average  size  of  building  lots  should  be  known. 
In  the  country  the  rod  and  the  mile  are  of  particular  importance  in  meas- 
uring the  size  of  fields  and  the  distance  to  the  village. 

WRITTEN  EXERCISE 

1.  How  many  feet  in  3  yd.  ?   How  many  inches  ? 

2.  How  many  feet  in  ^  mi.?  in  l  mi.?  in  ^  mi.? 

3.  How  many  rods  in  ^  mi.  ?  in  ^  mi.?  in  ^  mi.  ? 

4.  How  many  inches  in  1  yd.?  in  1  rd.?  in  1  mi.? 

5.  How  many  miles  in  640  rd.?  in  5440  rd.? 

6.  How  many  yards  in  792  ft.?  in  1065  ft.? 


234  MEASURES 

ORAL  EXERCISE 

1.  Estimate  the  length  and  the  width  of  this  room. 

2.  How  high  is  the  chalk  rack  from  the  floor  ? 

3.  How  high  do  you  think  the  door  is  ? 

4.  How  wide  do  you  think  the  street  is  in  front  of  the 
schoolhouse  ? 

5.  How  many  inches  do  you  step  in  taking  a  long  step  ? 

6.  Tell  some  place  that  is  about  a  mile  from  the  school- 
house. 

Teachers  should  make  sure  that  the  pupils  have  a  definite  idea  of  the 
value  of  each  item  in  the  various  tables,  and  should  fix  these  ideas  of  values 
by  frequent  reviews  and  drills  in  which  the  words  are  used  concretely. 
They  should  use  the  blacjcboard,  the  schoolroom  floor,  and  the  school  yard 
to  illustrate  distances  and  areas.  The  pupils  should  learn  to  pace  dis- 
tances. The  distance  from  the  school  to  some  well-known  point  should 
be  fixed  as  a  standard  mile  to  which  the  pupils  can  refer  in  making 
estimates.  Much  practice  in  estimating  should  be  given,  and  the  estimates 
should  be  followed  by  actual  measurements. 

WRITTEN  EXERCISE 

1.  Find  the  number  of  ounces  in  14  lb. 

2.  Find  the  number  of  pounds  in  98  oz. 

3.  Find  the  number  of  quarts  in  17  gal. 

4.  Find  the  number  of  gallons  in  17  qt. 

5.  Find  the  number  of  pecks  in  28  bu. 

6.  Find  the  number  of  bushels  in  28  pk. 

7.  If  you  weigh  52  lb.,  how  many  ounces  do  you  weigh  ? 

8.  If  a  street  is  66  ft.  wide,  what  is  its  width  in  yards  ? 


SQUARE  MEASURE  235 

ORAL  EXERCISE 

1.  A  square  is  3  ft.  on  a  side ;  what  is  the  area? 

2.  What  is  the  area  of  a  square  that  is  12  in.  on  a  side? 

3.  How  many  feet  in  1  yd.  ?   Then  1  ft.  is  what  part  of 
1  yd.  ?   How  many  square  feet  in  1  sq.  yd.  ? 


Square  Measure.    The  following  is  the  table  of  square 
measure : 
/      144  square  inches  (sq.  in.)  =  1  square  foot  (sq.  ft.) 
>7^  9  square  feet  =  1  square  yard  (sq.  yd.) 

3l'.  30|  square  yards  =  1  square  rod  (sq.  rd.) 

^  160  square  rods  =  1  acre  (A.) 

640  acres  =  1  square  mile  (sq.  mi.) 

In  the  country  special  care  should  be  taken  to  visualize  the  acre  by 
pointing  out  fields  that  contain  an  acre  or  a  definite  number  of  acres.  The 
teacher  should  review  page  151  at  this  time. 

WRITTEN  EXERCISE 

1.  How  many  times  is  9  sq.  ft.  contained  in  144  sq.  ft.? 
How  many  square  yards  in  144  sq.  ft.? 

2.  How  many  square  yards  in  an  oblong  30  yd.  long  and 
8  yd.  wide  ?   Draw  the  figure,  using  \  in.  to  a  yard. 

We  speak  of  such  a  rectangle  as  being  8  yd.  by  30  yd.  in  size. 

Find  the  areas  of  the  following  rectangles  : 

3.  32  ft.  by  52  ft.         6.  19  yd.  by  37  yd. 

4.  58  yd.  by  63  yd.        7.  43  ft.  by  98  ft. 

5.  16  ft.  by  121  ft.        8.  69  ft.  by  248  ft. 


286  MEASUKES 

ORAL  EXERCISE 

1.  If  you  were  to  speak  of  the  length  of  your  state, 
would  you  speak  of  it  by  miles  or  by  feet? 

2.  If  you  were  to  measure  your  schoolroom,  would  you 
measure  by  miles,  or  by  feet,  or  by  inches  ? 

3.  If  you  were  to  measure  your  finger,  would  you  meas- 
ure by  yards,  or  by  feet,  or  by  inches  ? 

4.  If  asked  your  age,  would  you  answer  in  years  or  in 
weeks?  If  asked  how  long  before  you  go  home  to-day,  how 
would  you  answer  ?     

Unit  of  Measure.  When  we  measure  anything  by  feet  we 
call  the  foot  the  unit  of  measure.  So  if  we  measure  weight 
by  the  pound,  the  pound  is  the  unit  of  measure. 

In  measuring  great  lengths  we  use  the  mile  as  the  unit. 
For  lengths  less  than  1  mi.  we  often  use  the  rod  or  the 
yard.    For  short  lengths  we  often  use  the  foot  or  the  inch. 

MEASURING 

1.  Measure  the  length  of  the  room,  using  1  ft.  as  the 
unit ;  using  1  yd.  as  the  unit. 

2.  Measure  the  length  of  the  desk,  using  1  ft.  as  the 
unit ;  using  1  in.  as  the  unit. 

3.  Measure  the  height  of  the  desk,  using  1  ft.  as  the 
unit ;  using  1  in.  as  the  unit. 

4.  Imagine  a  square  36  in.  on  a  side.  Find  its  area, 
using  1  sq.  ft.  as  the  unit ;  also  using  1  sq.  yd.  as  the  unit ; 
also  using  1  sq.  in.  as  the  unit. 


J 


DEAWING  TO  SCALE  237 

DRAWING  TO  SCALE 

1.  If  we  draw  a  picture  of  a  doll's  house,  and  make  it 
J  as  long  and  J  as  high  as  the  house,  we  say  that  we  draw 
the  picture  to  the  scale  of  1  to  4,  or  to  the  scale  J. 

Every  inch  in  length  is  then  represented  by  J-  in. 

We  may  draw  to  other  scales.  If  we  represent  1  ft.  by 
1  in.,  we  say  that  we  draw  to  the  scale  of  1  in.  to  1  ft. 
Since  there  are  12  in.  in  1  ft.  we  also  say  that  we  draw 
to  the  scale  of  1  to  12,  writing  this  as  the  scale  -^-^. 

A  B 

I I 

The  line  AB  drawn  to  the  scale  \.      i I 

The  line  AB  drawn  to  the  scale  \.  I I 

The  line  AB  drawn  to  the  scale  \.  I 1 


2.  If  we  draw  to  the  scale  ^,  by  what  length  shall  we 
represent  a  line  4  in.  long  ? 

3.  If  we  draw  to  the  scale  ^,  by  what  length  shall  we 
represent  a  line  12  in.  long  ?  a  line  15  in.  long  ? 

4.  If  we  draw  to  the  scale  J,  by  what  length  shall  we 
represent  a  line  40  in.  long?  a  line  36  in.  long? 

5.  Draw  a  hne  to  the  scale  J  to  represent  16  in. 

Draw  lines  to  the  given  scales  to  represent  these  lengths : 

6.  10  in.,  1  9.  24  in.,  J.  12.  20  in.,  ^. 

7.  15  in.,  J.  10.  24  in.,  J.  13.  30  in.,  ^. 

8.  12  in.,  1  11.  24  in.,  f  14.  36  in.,  f 

We  frequently  write  4'  for  4  ft.,  4"  for  4  in.,  4'  8"  for 
4  ft.  8  in.,  and  so  on. 


238 


MEASURES 


ORAL  EXERCISE 


1.  Here  is  a  rectangle  2"  long  by  1"  wide.  It  is  di- 
vided into  eight  squares,  each  of  which  is  J"  on  a  side. 

If  we  make  a  drawing  of  this  rectangle,  making  each 
line  half  as  long  as  it  is 


here,  we  have  the  lower 
rectangle.  We  then  say 
that  we  have  drawn  the 
rectangle  to  the  scale  ^, 
or  1  to  2,  or  1"  to  2". 

2.  A  plan  of  a  box  lid  is 
drawn  to  the  scale  ^.    The  drawing  is  4" 
long.   What  is  the  length  of  the  box  lid  ? 

3.  In  a  plan  of  a  room  the  scale  is  1" 
tol'.  The  plan  is  14"  by  16".  What  is  the  size  of  the  room  ? 

4.  A  drawing  is  made  of  a  leaf  of  a  notebook.  The 
drawing  is  2"  by  3"  and  the  scale  is  -J.  What  are  the  di- 
mensions of  the  leaf  ? 

5.  A  drawing  is  made  of  the  cloth  back  used  in  binding 
a  book.  The  drawing  is  1"  by  3"  and  the  scale  is  J.  What 
are  the  dimensions  of  the  cloth  ? 


WRITTEN  EXERCISE 

1.  Make  the  drawing  mentioned  above  in  Ex.  2. 

2.  Make  the  drawing  mentioned  above  in  Ex.  3. 

3.  Make  the  drawing  mentioned  above  in  Ex.  4. 

4.  Make  the  drawing  mentioned  above  in  Ex.  5. 


AREAS  /    '  239 

WRITTEN  EXERCISE 

Find  the  areas  of  the  following  rectangles : 

1.  6  ft.  by  17  ft.  8.  19  ft.  by  72  ft. 

2.  12  ft.  by  27  ft.  9.  32  in.  by  47  in. 

3.  21  in.  by  53  in.  10.  67  in.  by  82  in. 

4.  12  yd.  by  25  yd.  11.  33  yd.  by  47  yd. 

5.  26  yd.  by  48  yd.  12.  54  ft.  by  96  ft. 

6.  22  yd.  by  75  yd.  13.  29  in.  by  38  in. 

7.  23  rd.  by  75  rd.  14.  43  mi.  by  62  mi. 

15.  Draw  a  picture  of  a  square  2  ft.  on  a  side,  using  J  in. 
to  represent  a  foot. 

This  IS  called  drawing  to  a  scale  of  i-  in,  to  1  ft.  •' 

16.  Draw  a  picture  of  a  rectangle  2  yd.  wide  and  3  yd. 
long,  on  a  scale  of  1  in.  to  the  yard. 

17.  It  is  32  in.  around  a  square.  What  is  the  length 
of  each  side?  How  many  square  inches  does  the  square 
contain  ? 

18.  A  farmer  has  a  field  40  rd.  long  and  16  rd.  wide. 
How  many  square  rods  does  it  contain? 

19.  A  sidewalk  is  95  ft.  long  and  5  ft.  wide.  How  many 
square  feet  of  area  in  the  walk  ? 

20.  A  garden  is  14  rd.  long  and  7  rd.  wide.  What  is  its 
area  in  square  rods  ? 

If  the  class  has  not  learned  the  meaning  of  right  angle,  acute  angle, 
and  obtuse  angle,  these  should  be  explained  before  proceeding  to  page  240. 
The  terms  "horizontal,"  "  vertical,"  and  "perpendicular"  should  also  be 
explained  at  this  time. 


240  MEASURES 

ORAL  EXERCISE 

1.  Which  of  these  three  triangles  has  an  obtuse  angle  ? 
What  kind  of  a  triangle  is  it  ? 


2.  Which  of  these  triangles  has  a  right  angle  ?  Point  to 
the  right  angle.    What  kind  of  a  triangle  is  it  ? 

3.  In  which  of  the  triangles  are  all  of  the  angles  acute  ? 
What  kind  of  a  triangle  is  it  ? 

4.  What  kind  of  a  triangle  can  you  make  with  three 
narrow  strips  of  paper  3  in.,  4  in.,  and  5  in.  long  ? 


Triangles.  A  triangle  having  a  right  angle  is  a  right 
triangle. 

A  triangle  having  an  obtuse  angle  is  an  obtuse  triangle. 
A  triangle  having  three  acute  angles  is  an  acute  triangle. 

The  pupils  should  have  plenty  of  practice  in  drawing  these  figures. 
WRITTEN  EXERCISE 

1.  How  far  is  it  around  a  triangle  whose  sides  are  14  ft., 
12  ft.,  and  12  ft.? 

2.  Draw  any  acute  triangle  with  two  of  its  sides  2  in. 
and  3  in.  Measure  the  third  side  and  find  how  far  it  is 
around  the  triangle. 

3.  Draw  a  right  triangle  with  the  shortest  side  1 J  in.,  and 
the  next  longer  side  2  in.  Measure  and  find  the  length  of 
the  longest  side. 


VOLUMES 


241 


ORAL  EXERCISE 

1.  How  many  cubic  inches  are  there  in  a  block  1  in.  long, 
1  in.  wide,  and  1  in.  high  ? 

2.  How  long  is  the  edge  of  a  cube  which  con- 
tains 1  cu.  in.  ?  How  long  is  the  edge  of  a  cube 
which  contains  1  cu.  ft.  ? 

We  write  cu.  in.  for  cubic  inches  and  cu.  ft.  for  cubic  feet. 

3.  How  many  cubic  inches  are  there  in  a  block  3  in.  long, 

1  in.  wide,  and  1  in.  high  ? 

The  teacher  should  use  three  1-inch  cubes,  or  should  draw  the  figure. 

4.  How  many  cubic  inches  are  there  in  a  block  3  in.  long, 

2  in.  wide,  and  1  in.  high  ? 

The  teacher  should  use  six  1-inch  cubes,  or  should  draw  the  figure. 

5.  How  many  cubic  inches  are  there  in  a  block  3  in.  long, 
2  in.  wide,  and  4  in.  high  ? 

Since  a  block  1  in.  long,  1  in.  wide, 
and  1  in.  high  contains  1  cu.  in.,  a 
block  3  times  as  long  contains  3  x 

1  cu.  in.,  or  3  cu.  in.,  and  a  block  2 
times  as  wide  contains  2  x  3  cu.  in.,  or  6  cu.  in.,  and  a  block 
4  times  as  high  contains  4  x  6  cu.  in.,  or  24  cu.  in.   That  is, 

2  X  3  X  4  cu.  in.  =  24  cu.  in. 

6.  How  many  cubic  inches  are  there  in  a  block  3  in.  long, 

2  in.  wide,  and  2  in.  high  ? 

The  teacher  should  see  that  the  pupils  understand  informally  the  mean- 
ing of  the  words  cube,  solid,  volume,  and  dimensions,  and  should  state  to  the 
class  that  the  blocks  and  boxes  which  we  shall  measure  have  square  cor- 
ners.  Such  a  long  term  as  rectangular  solid  need  not  be  used  at  this  time. 


242 


MEASUEES 


ORAL  EXERCISE 

1.  The  cube  A  is  how  many  times  the  block  5? 

2.  The  block  B  is  how  many  times  the  cube  0  ? 

3.  A  cube  that  is  3  ft.  on  an  edge  is  how  many  times  as 
large  as  a  cube  that  is 


1  ft.  on  an  edge? 

4.  How  many  feet  in 
1  yd.?    Then  how  many    LLL^^^ 
cubic  feet  in  1  cubic  yard  ?  ^  b  c 

5.  How  would  you  find  the  number  of  cubic  inches  in 
1  cu.  ft.  ?  Multiply  on  the  blackboard  and  find  this  number. 


Cubic   Measure.    The   following   is   the    table  of  cubic 
measure : 

1728  cubic  inches  (cu.  in.)  =  1  cubic  foot  (cu.  ft.) 
27  cubic  feet  =  1  cubic  yard  (cu.  yd.) 

WRITTEN  EXERCISE 

1.  A  bin  is  3  ft.  by  5  ft.  by  2  ft.    It  holds  how  much 
more  than  1  cu.  yd.  ? 

2.  A  box  is  8  in.  by  20  in.  by  10  in.    It  holds  how  much 
less  than  1  cu.  ft.  ? 

3.  How  many  cubic  yards  in  a  bin  6  ft.  by  9  ft.  by  3  ft.  ? 

Find  the  volume  of  solids  whose  dimensions  are : 

4.  12  in.,  19  in.,  14  in.  6.  6  ft.,  138  ft.,  2  ft. 

5.  27  in.,  43  in.,  32  in.  7.  2  yd.,  698  yd.,  1  yd. 


VOLUMES  243 

ORAL  EXERCISE 

1.  How  many  cubic  feet  in  10  cu.  yd.  ? 

2.  How  many  cubic  yards  in  a  cellar  5  yd.  by  10  yd. 
by  2  yd.  ?   in  a  cellar  4  yd.  by  5  yd.  by  3  yd.  ? 

3.  How  many  cubic  inches  in  a  box  3  in.  by  4  in.  by 
5  in.  ?   in  a  box  4  in.  by  5  in.  by  7  in.  ? 

4.  Hx)w  many  cubic  inches  in  a  cube  2  in.  on  an  edge  ? 

State  the  volume  of  boxes  of  the  following  dimensions : 

5.  2  in.,  3  in.,  5  in.  9.  4  in.,  5  in.,  6  in. 

6.  3  in.,  4  in.,  10  in.  10.  5  in.,  7  in.,  6  in. 

7.  2  in.,  5  in.,  10  in.  11.  4  in.,  5  in.,  10  in. 

8.  2  in.,  4  in.,  6  in.  12.  3  in.,  5  in.,  10  in. 

WRITTEN  EXERCISE 

1.  How  many  cubic  inches  in  an  aquarium  16  in.  long, 
8  in.  wide,  and  9  in.  deep  ? 

2.  How  many  cubic  feet  in  a  wall  36  ft.  long,  30  ft.  wide, 
and  2  ft.  thick  ? 

3.  A  cistern  is  6  ft.  square  at  the  bottom  and  5  ft.  deep. 
How  many  cubic  feet  of  water  will  it  contain  ? 

4.  A  water  tank  is  8  ft.  long,  6  ft.  wide,  and  4  ft.  deep. 
How  many  cubic  feet  of  water  will  it  contain? 

5.  A  cellar  is  to  be  dug  19  ft.  by  25  ft.  by  6  ft.    How 
many  cubic  feet  of  earth  must  be  taken  out  ? 

6.  A  coal  bin  is  22  ft.  long,  15  ft.  wide,  and  7  ft.  deep. 
How  many  cubic  feet  of  coal  will  it  contain? 


244 


MEASURES 
ORAL  EXERCISE 


1.  This  boy  is  4  ft.  tall.    Estimate  the  dimensions  of  this 
woodpile.    Do  you  know  the  name  of  this  amount  of  wood? 


2.  A  pile  of  wood  is  8  ft.  long,  4  ft.  wide,  and  4  ft.  high. 
How  do  you  find  the  number  of  cubic  feet  it  contains  ? 


Eead  and  learn  this  table : 

128  cubic  feet  =  1  cord  (cd). 

Wood  is  sold  by  the  cord.  Stand  8  ft.  from  the  front  of 
the  room  and  4  ft.  from  the  side,  and  hold  your  hand  4  ft. 
from  the  floor,  so  as  to  show  the  size  of  a  cord. 


3.  How  much  will  9  cd.  of  wood  cost  at  $4  a  cord? 

4.  How  much  will  7  cd.  of  wood  cost  at  $5  a  cord  ? 

5.  How  many  cords  of  wood  in  a  pile  16  ft.  long,  4  ft. 
wide,  and  8  ft.  high  ? 


MEASURES  OF  WEIGHT  245 

ORAL  EXERCISE 

1.  Meat  is  sold  by  the  pound.  Candy  is  sold  by  the  pound. 
Pepper  is  sold  by  the  ounce.  Do  you  know  how  coal  is 
sold  ?  Do  you  know  how  hay  is  sold  ? 

2.  Can  you  name  anything  else  that  is  sold  by  the  ounce  ? 
by  the  pound  ?  by  the  ton  ? 

3.  How  many  ounces  are  there  in  a  pound?  How  many 
pounds  in  a  ton  ? 

Weight.    The  following  is  the  table  of  weight : 
16  ounces  (oz.)=l  pound  (lb.) 
2000  pounds  =1  ton  (T.) 
The  ton  is  used  in  weighing  substances  sold  in  heavy 
loads,  like  coal,  hay,  building  stone,  and  iron. 

WRITTEN  EXERCISE 

1.  At  $12.75  a  ton,  what  will  17  T.  of  hay  cost? 

2.  At  $5.50  a  ton,  what  will  34  T.  of  coal  cost  ? 

3.  At  $36.60  for  6  T.,  what  will  1  T.  of  coal  cost? 

4.  When  coal  is  worth  $7.25  a  ton,  what  will  9  T.  cost? 

5.  When  hay  is  worth  $13.25  a  ton,  what  will  7  T.  cost  ? 
14  T.?  19  T.?  28  T.?  37  T.?  49  T.? 

6.  What  will  17  T.  of  coal  cost  at  $4.75  a  ton  ? 

7.  What  will  26  T.  of  coal  cost  at  $4.95  a  ton  ?  at  $5.30 
a  ton?  at  $5.80  a  ton?  at  $6.25  a  ton? 

8.  What  does  hay  cost  a  ton  when  9  T.  cost  $116.10? 

9.  What  is  hay  worth  when  21  T.  cost  $270.90  ? 


246 


USING  WHAT  YOU  HAVE  LEARNED 


VII.    USING  WHAT  YOU  HAVE  LEARNED 


A  BOY  SCOUT  CLUB 

1.  These  Boy  Scouts  earned  the  money  for  their  uni- 
forms. The  hats  cost  $1.15  each,  the  coats  $1.25,  the 
trousers  $1,  the  leggings  55^,  and  the  shirts  $1.  Find  the 
cost  of  the  suits  for  the  five  boys  shown  in  the  picture. 

2.  The  patrol  leader  decided  to  add  to  his  outfit  a  belt 
at  40^,  a  canteen  at  50^,  and  a  haversack  at  75^.  He 
handed  the  salesman  a  $2  bill.    What  change  was  due  ? 

3.  For  their  hikes  they  bought  a  stewpan  at  80^,  a 
water  pail  at  25^,  a  coffeepot  at  60^,  and  a  ring  stand 
at  20^.   How  much  did  they  pay  for  all  these  ? 

4.  For  luncheon  one  day  they  took  Frankfurters  at  30^, 
buns  at  18^,  mustard  at  5(^,  pie  at  20  (^,  and  2  qt.  of  milk 
at  8^  a  quart.  Each  boy  paid  10^  for  car  fares.  How  much 
did  the  five  boys  pay  in  all  ? 


SCOUT  CAMP  247 

GOING  TO  SCOUT  CAMP 

1.  The  patrol  of  a  Scout  company  consists  of  8  boys. 
They  raised  money  by  an  entertainment  to  go  into  camp 
for  two  weeks.  They  took  in  |62.40,  and  their  expenses 
were  $4.80.  How  much  was  left  for  going  to  camp  ?  What 
was  each  boy's  share?  How  much  more  must  each  boy 
earn  to  start  out  with  $12  ? 

2.  Each  boy's  expenses  were  as  follows:  railway  fare, 
$1.04;  fare  on  the  boat,  $1;  street  car,  15^;  meals,  going 
and  returning,  78^;  camp  fee,  $7.84.  What  was  the  total 
cost  for  each  boy  ?  What  was  the  total  cost  for  the  patrol  ? 

3.  If  each  boy  started  with  $15,  how  much  had  he  left  for 
spending  money  after  paying  his  share  as  found  in  Ex.  2  ? 

4.  One  boy  lost  a  $5  bill  on  the  way  to  camp.  You 
have  found  in  Ex.  2  the  total  cost  for  each  boy.  Now  tell 
how  much  he  must  borrow  from  the  others  to  make  up 
his  expenses, 

5.  One  of  the  boys  became  ill  and  had  to  return  home 
at  the  end  of  a  week.  How  much  should  he  receive  back 
on  his  camp  fee? 

6.  There  were  84  boys  in  camp.  If  the  fee  of  each  was 
$7.84,  what  was  the  total  amount  paid  in  camp  fees? 

7.  The  boys  walked  3|-  mi.  from  the  station  to  the  camp 
grounds  at  Scout  pace,  which  is  1  mi.  in  12  min.  How  long 
did  it  take  to  go  this  distance  ? 

Find  3  X  12  min.,  then  |  of  12  min.,  and  then  add  the  results. 

8.  If  a  patrol  starts  on  a  hike  at  15  min.  before  10  and 
returns  at  10  min.  after  12,  how  long  are  the  boys  out  ? 


248  FRACTIONS 

VIII.   FRACTIONS 

Terms  of  a  Fraction.  To  take  |  of  this  rectangle,  we  divide 
the  rectangle  into  8  equal  parts  and  take  3  of  these  parts. 

In  the  fraction  f ,  the  number  3  is 
called  the  numerator^  and  it  tells  how 
many  equal  parts  we  take. 

In  the  same  fraction  8  is  called  the 


denominator,  and  it  tells  the  number  of  equal  parts  into 
which  the  rectangle  has  been  divided. 

3  =    numerator 

8  =  denominator 

The  numerator  and  denominator  are  called  the  terms  of 
the  fraction.    The  terms  of  the  fraction  f  are  3  and  8. 

A  whole  number,  Hke  2,  7,  or  $10,  is  called  an  integer. 

An  integer  and  a  fraction  together  are  called  a  mixed 
number;   as  21,  $4J. 

A  fraction  that  is  less  than  1  is  called  a,  proper  fraction ; 

^^  2'  h  f  • 

A  fraction  that  is  equal  to  1  or  greater  than  1  is  called 

an  improper  fraction ;  as  f,  f,  f,  ^. 

We  see  that  we  can  write  improper  fractions  as  whole 

numbers  or  as  mixed  numbers.    For  example, 

This  work  in  fractions  covers  what  is  usually  given  in  Grade  IV.  It  is 
slightly  more  extended  than  that  required  by  the  minimum  course  of  study 
in  some  places  and  may,  therefore,  be  shortened  if  the  teacher  desires.  It 
is  given  in  this  form  so  that  teachers  who  wish  the  material  need  not  go 
outside  the  textbook  to  find  it, 


FRACTION  COLUMNS 
ORAL  EXERCISE 


249 


4 
4    4 

4    4    4 

4:       4:       4:       4: 

4    812l6 


5 

5    5 

5    5    5 

5    5    5    5 

5l0l5  20 


6 

6 

6 

6 

6 

6 

6    6 

6 

6 

6  12  18  24 

7 

7    7 

7    7    7 

7    7    7    7 

714  2128 


If  we  look  at  these  columns  and  the  sums,  we  see  that 
4  is  J  of  8,  12  is  J  of  16,  and  so  on. 


Point  to  the  columns  representing  the  following  numherSf 
and  tell  the  answers  in  all  cases : 

1.  10,  1  of  10,  f  of  10. 

2.  15, 1  of  15,  I  of  15. 

3.  14, 1  of  14,  I  of  14, 1  of  14. 

4.  21, 1  of  21,  I  of  21,  f  of  21. 

5.  28,  1  of  28,  f  (or  i)  of  28,  |  of  28. 

6.  12,  1  of  12,  f  of  12,  1  of  12. 

7.  18,  11  times  18,  i  of  18,  f  of  18. 

8.  Think  of  -J-  of  each  of  the  following  numbers,  and 
then  state  |-  of  each: 


9 


6       12 


21       30        33        36 


9.  Think  of  J-  of  each  of  the  following  numbers,  and 
then  state  f  of  each : 

32       40       12       24       20       28        36        44 


250  FRACTIONS 

ORAL  EXERCISE 

1.  How  much  is  |  of  12  ?   f  of  12  ? 

2.  How  much  is  1-  of  20  ?   f  of  20  ?   f  of  20  ? 

3.  How  much  is  1  of  12  ?   f  of  12  ?   i  of  12  ? 

Find  §,  and  then  §,  of  the  following : 

4.  18.       5.  15.        6.  24.        7.  39.       8.  33.        9.  60. 

Find  |,  and  then  |,  of  the  folloiving  : 

10.  15.     11.  25.     12.  35.     13.  45.     14.  50.     15.  55. 

WRITTEN   EXERCISE 

1.  Find  1  of  75,  and  then  find  f  of  75. 

2.  Find  i  of  72,  and  then  find  f  of  72. 

3.  Find  \  of  81,  and  then  find  |  of  81. 

Find  |,  and  then  |,  of  the  folloioing : 

4.  27.        5.  45.        6.  63.        7.  42.       8.  54.        9.  66. 

Find  I,  and  then  §  and  |,  of  the  following : 

10.  65.     11.  30.     12.  85.     13.  40.      14.  80.     15.  95. 

Usi7ig  a  ruler,  or  the  edge  of  a  piece  of  paper  on  lohich 
inches  have  been  marked,  draiv  lines  of  the  following  lengths, 
and  then  mark  off  the  parts  stated : 

16.  2  in.,  I  of  2  in.  19.  IJ  in.,  f  of  IJ  in. 

17.  11  in.,  f  of  11  in.  20.  21  in.,  l  of  21  in. 

18.  21  in.,  f  of  21  in.  21.  41  in.,  |  of  41  in. 


1 

1 

1 

\ 

FRACTIONAL  PARTS  251 

ORAL  EXERCISE 

1.  How  many  fourths  of  a  square  in  1  square?  How 
many  fourths  of  an  apple  in  1  apple?    How 

many  fourths  in  1  ? 

2.  How  many  fourths  of  a  square  in  J  of  the 
square?  How  many  fourths  of  anything  in  1 
of  it?  in  I  of  it?  in  |  of  it? 

3.  How  much  is  J  of  24  ?  |  of  24?  i  of  24?  How  does 
f  compare  with  i  ?  with  J  ? 

4.  How  do  you  find  ^  of  a  number  ?  Then  how  do  you 
find  1^  of  it  ?  |-  of  it  ?  Is  there  any  easier  way  of  finding  ^ 
of  a  number  ? 

5.  How  much  is  J  of  16  ?  |  of  16  ?  i  of  16  ? 

6.  How  much  is  J  of  48?  |  of  48?  1  of  48? 

7.  How  much  is  1  of  36  ?  f  of  36  ?  i  of  36  ? 

8.  Which  will  buy  the  more  candy,  a  half  dollar,  two 
quarters,  or  five  dimes  ?   Why  is  this  ? 

WRITTEN  EXERCISE 

Draw  lines  and  divide  them  into  parts  to  show  that : 


l-i=f 

*-f  =  i-        ■'■^  =  1        io-A  =  t 

2.  |  =  i. 

5-4  =  f        8-A  =  i-        ii-T%  =  i 

3-  l  =  f 

fil  —  3                  Q       6—3                  19        6—1 
*»•    2         6-                ^-10         5-                •^'*'    12         2" 

Draw  squares  and  divide  them  into  parts  to  show  that : 

13.  i  =  f. 

15.1  =  1           17.  1  =  |.             19.  |  =  f 

14.  f  =  |. 

16.  |=«.          18.  i  =  |.             20.  |  =  f. 

252 


FEACTIONS 


ORAL  EXERCISE 

1.  Look  at  figure  A  and  state  how  many  sixths  you  see 
in  one  half. 

2.  Look  at  figure  B  and  state 
how  many  eighths  you  see  in 
one  half ;  in  three  quarters. 

3.  Look  at  figure  C  and  state  how  many  tenths  you  see 
in  one  half ;  in  one  fifth ;  in  four  fifths. 


Reduction.  We  see  that  f  can  be  obtained  from  ^  by 
multiplying  both  terms  by  2,  and  that  ^  can  be  obtained 
from  -^  by  dividing  both  terms  by  5.    That  is, 

Both  terms  of  a  fraction  may  he  multiplied  hy  the  same 
number  without  changing  the  value  of  the  fraction. 

Both  terms  of  a  fraction  m.ay  he  divided  hy  the  same 
numher  without  changing  the  value  of  the  fraction. 

When  we  change  the  value  of  the  terms  without  chang- 
ing the  value  of  a  fraction  we  reduce  the  fraction. 

When  both  terms  cannot  be  divided  by  the  same  number, 
the  fraction  is  said  to  be  in  lowest  terms. 

To  reduce  a  fraction  to  loivest  terms,  divide  hy  the  largest 
numher  that  will  divide  both  terms  ivithout  a  remainder. 


12 


rr^ — 7  =  -T ,  lowest  terms. 
iz  ^  4     o 


In  this  example,  4  is  said  to  be  canceled 
from  both  terms  when  the  work  is  written 
as  here  shown. 


REDUCTION  253 

WRITTEN  EXERCISE 

1.  Reduce  the  following  fractions  to  halves  : 

2  4  8.  JL2_  1_6_  2_4  _3_2.  40. 

4888  8  8  8  8" 

2.  Reduce  the  following  fractions  to  fourths : 

1  2  4  1_6  1_0  2_0  1_8_  23. 

2888  8  8"  8  8 

3.  Reduce  the  following  fractions  to  eighths  : 

1  1  3.  4  6  1  _2_  _i_ 

2  4  4  4  4  2  16  16 

4.  Reduce  the  following  fractions  to  twelfths : 

113.1  2.1  5.  _2_ 

244  3'  3  6  6  24 

5.  Reduce  the  following  fractions  to  lowest  terms  : 

2.  4  JJI         _8_  3.  4  6.  5 

488  10  6  6  8  TO" 

6.  Express  ^  in.  and  ^  in.  as  sixths  of  an  inch,  and  tell 
which  is  the  greater. 

7.  Express  J  in.  and  J  in.  as  twelfths  of  an  inch,  and  tell 
which  is  the  greater. 

8.  Express  as  sixths :  J,  ^,  and  -f. 

9.  Express  as  tenths :  ^,  \,  |-,  |-,  and  ^. 

10.  Express  as  fifteenths :  \,  J,  f,  ^,  f,  and  f. 

11.  Express  as  sixteenths :  1,  J-,  -J,  J,  |,  and  f. 

12.  Express  |-  as  halves ;  as  fourths  ;  as  sixteenths. 

13.  Reduce  f  to  halves ;  to  fourths ;  to  sixteenths. 

14.  How  many  fourths  in|?  in^?  in|^? 

15.  How  many  eighths  in  -|  ?  in  ^  ?  in  1  ? 

16.  How  many  tenths  in  ^^^  ?  in  J  ?  in  1  ? 


254  FRACTIONS 

Addition.  If  we  ask  for  the  sum  of  3  boys  and  2  girls, 
the  answer  cannot  be  boys  alone,  or  girls  alone.  But  we  say, 

3  boys  =  3  children 
2  girls  =  2  children 

5  children  in  all 

In  addhig,  loe  think  of  things  as  having  the  same  name. 

In  the  same  way,  if  we  wish  to  find  the  sum  of  J  and  |, 
we  must  think  of  these  as  J  and  J,  the  sum  being  |,  or  1  J. 

In  adding  fractions  xoe  think  of  them  as  having  the  same 
name. 

ORAL  EXERCISE 

1.  Express  J  as  eighths.   To  the  result  add  f . 

2.  If  you  are  making  the  supports  for  a  bookshelf  and 
fasten  a  strip  of  molding  i  in.  thick  to  a  strip  of  wood  f  in. 
thick,  how  thick  are  the  two  together  ? 

3.  Express  J  as  tenths.   To  the  result  add  ^, 

4.  If  you  lay  an  arithmetic  that  is  ^  in.  thick  on  a  note- 
book that  is  3^  in.  thick,  how  thick  are  the  two  together  ? 

5.  Express  f  as  sixths.   To  the  result  add  J-. 

6.  If  you  sew  a  piece  of  cloth  ^  yd.  wide  to  a  strip  J  yd. 
wide,  how  wide  will  the  new  piece  be  ? 

WRITTEN  EXERCISE 

Reduce  to  the  same  denominator  and  add : 

1.  J,  }.  3.  i,  f  5.  i,  -J.  7.  i,  J. 

2.  h  f  4-  h  f  •  6-  h  h  8.  f ,  J. 


ADDITION  255 

Addition  of  Fractions.  Margaret  had  a  lily  given  to  her 
when  it  was  only  3|in.  tall.  After  it  had  grown  to  be 
7^  in.  taller,  how  tall  was  the  lily  ? 

We  see  that  we  must  add  3|^  in.  and  7|-  in. 

We  found  on  page  254  that  we  must  think  of  the  frac- 
tions as  having  the  same  denominator. 

Teachers  may,  if  they  choose,  speak  of  reducing  the  fractions  to  the 
least  common  denominator,  or  to  fractions  having  the  least  common  de- 
nominator.   It  is  well,  however,  to  use  simple  language  at  this  time. 

In  adding  3  J  and  7|-,  we  might  think  of  both  fractions 
as  12ths  or  as  24ths.  But  to  save  work  it  is  better  to  use 
fractions  having  as  small  a  denom- 
inator as  possible. 

If  we  think  of  the  numbers 
which  can  be  exactly  divided  by 
both  4  and  6,  we  see  that  the 
smallest  is  12.  We  know  this  be- 
cause no  number  less  than  12  is  exactly  divisible  by  4  and  6. 

Therefore  the  smallest  denominator  that  both  fractions 
can  have  is  12. 

We  also  see  that  f  =  3^  and  that  f  =  J^,  because  we  may 
multiply  both  terms  of  f  by  3,  and  both  terms  of  f  by  2. 

Then  the  sum  is  10^,  which  equals  10  + 1^,  or  H^^. 

So  the  hly  grew  to  be  llj^  in.  tall. 

The  pupil  is  not  expected  to  explain  an  example  like  this  at  present. 
Gradually,  as  here  and  on  page  211,  he  should  be  led  to  add  fractions  in 
cases  where  the  least  common  denominator  can  be  seen  by  inspection. 
Unusual  denominators,  such  as  7,  11,  and  13,  should  not  be  used  at  this 
time.  Even  the  illustrative  problem  given  above,  desirable  as  it  is  for 
purposes  of  illustration,  is  more  difficult  than  is  usually  needed  in  business. 


Q3  _  Q  9 

4  ~"  ^12" 

75.  —  710. 
'6  'l2 


1019  =  11^- 
^^12         -^-^12 


256  FRACTIONS 

WRITTEN  EXERCISE 

1.  Add  21  lb.,  61  lb.,  and  IJ  lb. 

2.  Add  11  yd.,  11  yd.,  and  21  yd. 

3.  The  top  of  a  teacher's  desk  is  41  ft.  long  and  3  ft. 
wide.  What  is  the  perimeter,  that  is,  the  distance  around 
the  top  of  the  desk  ? 

4.  Some  boys  built  a  hut  7J-  ft.  long  and  5  ft.  wide. 
What  was  the  perimeter  ? 

5.  If  a  boy  in  this  class  weighs  66|-  lb.,  and  his  dog 
20 J  lb.,  how  much  do  they  weigh  together? 

6.  A  lady  bought  three  pieces  of  cloth,  containing 
17f  yd.,  16J  yd.,  and  23J  yd.,  respectively.  How  many 
yards  did  she  buy  ? 

7.  One  pole  is  10 J  ft.  long,  another  10|^  ft.,  a  third 
lOj^  ft.,  and  a  fourth  3  ft.  What  is  their  total  length 
when  placed  end  to  end? 

8.  A  man  has  168 J  acres  of  land.  He  buys  31  acres 
from  one  neighbor  and  49|^  acres  from  another.  How  many 
acres  does  he  then  own  ? 

9.  A  kite  string  was  broken,  and  four  parts  were  saved. 
The  first  was  751  ft.  long,  the  second  127f  ft.,  the  third 
261  ft.,  and  the  fourth  89i  ft.  Allowing  1  ft.  for  tying, 
how  long  was  the  string  when  all  four  were  tied  together  ? 

10.  Five  cans  of  sirup  were  measured  carefully  and 
the  first  was  found  to  contain  21  qt.,  the  second  2 J  qt., 
the  third  2Jg-  qt.,  the  fourth  2f  qt.,  and  the  fifth  2J  qt. 
How  many  quarts  were  there  in  all  ? 


SUBTRACTION  267 

Subtraction  of  Fractions.  Mollie  had  a  little  rosebush 
given  to  her.  It  was  then  only  3|^  in.  tall.  After  it  had 
grown  to  be  18|-  in.  tall  her  mother  asked 
her  how  much  it  had  grown.  What  should 
Mollie  answer? 

We   see   that   Molhe   must    subtract 


18f  =  18it 
3f=    83-% 


3|- in.  from  18|- in.  1^ 

In  subtraction,  as  in  addition,  we  must 
think  of  the  fractions  as  having  the  same  denominator. 

The  smallest  denominator  that  we  can  use  is  12. 

We  see  that  |-  =  ^,  and  that  f  =  ^. 

Then  18f  -^  =  18lf  -  S^^  =  Ib^. 

So  Mollie  should  say  that  her  bush  had  grown  IS^^^in. 

WRITTEN  EXERCISE 

1.  If  from  a  board  J|-  in.  thick  we  plane  off  3^  in.,  how 
thick  is  the  board  then  ? 

2.  If  a  notebook  is  -^  in.  thick  and  the  cover  is  3^^.  in. 
thick,  how  thick  is  the  book  without  the  cover? 

3.  If  from  a  board  ^  in.  thick  we  plane  off  \  in.,  how 
thick  is  the  board  then  ? 

Subtract  the  following : 


4. 

1  —  1 

2  3- 

9. 

1  _  1 

2  ^' 

14. 

3|  in. -11  in. 

5. 

1-4- 

10. 

l-h 

15. 

4  J  in.  -  2|  in. 

6. 

i-4- 

11. 

i-i- 

16. 

5J  yd. -21  yd 

7. 

1  _  1 

2  4- 

12. 

i-h 

17. 

71  yd. -3J  yd 

8. 

2._  1 
3          2- 

13. 

l-i- 

18. 

8f  in. -41  in. 

258  ALIQUOT  PAETS 

IX.   ALIQUOT  PAETS 
WRITTEN  EXERCISE 

1.  Multiply  246  by  5.   Divide  2460  by  2.   Compare  the 
results. 

2.  Instead  of  multiplying  by  5,  you  may  annex  how 
many  zeros  and  divide  by  what  number  ? 

3.  Multiply  224  by  25.    Divide  22,400  by  4.    Compare 
the  results. 

4.  Instead  of  multiplying  by  25,  you  may  annex  how 
many  zeros  and  divide  by  what  number  ? 


To  multvply  hy  5,  annex  a  zero  and  divide  hy  2. 
To  multiply  hy  25,  annex  two  zeros  and  divide  hy  4. 


5.  Divide  240  by  5.    Multiply  24  by  2.    Compare  the 
results. 

6.  Instead  of  dividing  tens  by  5,  you  may  cut  off  how 
many  zeros  and  multiply  by  what  number  ? 

7.  Divide  300  by  25.    Multiply  3  by  4.    Compare  the 
results. 

8.  Instead  of  dividing  hundreds  by  25,  you  may  cut  off 
how  many  zeros  and  multiply  by  what  number  ? 


To  divide  tens  hy  5,  cut  off  a  zero  and  multiply  hy  2. 
To  divide  hundreds  hy  25,  cut  off  two  zeros  and  mul- 
tiply hy  4. 


MULTIPLICATION  259 

ORAL  EXERCISE 

Multiply  the  following : 

1.  86  by  5.       3.  84  by  25.      5.  88  by  25. 

2.  44  by  25.      4.  48  by  25.      6.  124  by  5. 

Divide  the  following : 

7.110-5.  8.320-^-5.  9.800-25. 


Aliquot  Part.  An  integer  or  a  mixed  number  that  will 
exactly  divide  a  number  is  called  an  aliquot  part  of  that 
number.    Thus, 

10.50  is  1  of  $1  $0,331  is  1  of  $1 

$0.25  is  1  of  $1  $0.66f  is  |  of  $1 

$0,121  is  1  of  $1  $0.20  is  1  of  $1 

Hence,  instead  of  multiplying  $0,121  by  16^  ^e  may 
simply  multiply  $|-  by  16,  which  is  much  easier. 

Teachers  should  show  the  pupils  that  16  x  f  |  gives  the  same  answer  as 
\  of  $16,  and  is  an  easier  operation.  They  should  also  recognize  that  it  is 
not  necessary  to  label  the  numbers  except  when  it  adds  to  the  clearness  of 
a  solution.    That  is,  we  may  write  "16  x  \  =  2,"  the  number  of  dollars. 

WRITTEN  EXERCISE 

Multiply  the  following : 


1. 

32  X  $0,121 

2. 

64  X  $0,121 

3. 

56  X  $0.50. 

4. 

72  X  $0.25. 

5. 

96  X  $0,331 

6. 

120  X  $0.66f , 

7. 

375  X  $0,331 

8. 

336  X  $0.25. 

9. 

336  X  $0,331 

10. 

666  X  $0,331 

260  BILLS  AND  EECEIPTS 

X.   BILLS  AND  EECEIPTS 
ORAL  EXERCISE 

1.  What  is  meant  by  charging  goods  at  a  store  ? 

2.  What  is  meant  by  having  an  account  at  a  store  ? 

3.  What  is  meant  by  a  bill  of  goods  bought  at  a  store  ? 

4.  What  does  this  item  mean:   "  8  doz.  eggs  @  30^"? 


Making  out  Bills.  To  foot  a  hill  means  to  add  the  amounts 
and  find  the  total  cost.  To  receipt  a  hill  means  to  stamp  or 
write  the  words  "  Paid  "  or  "  Received  Payment,"  followed 
by  the  date  and  by  the  name  of  the  one  to  whom  it  is  due. 
This  is  a  receipted  bill : 

Newark,  N.J.,  March  1,  1919 
Mr.  David  Brownson 

Bought  of  CHARLES  DUNHAM 

Fd>.  \    6    \  6  cans  soup  @  20 p  ||       1  \  20 

Received  Payment,  March  S,  1916 


5.  Study  the  bill  and  answer  these  questions :  What 
does  @  mean?  What  is  the  amount  of  the  bill?  When 
were  the  goods  bought?  When  was  the  bill  paid?  Who 
was  the  buyer  ?  Who  was  the  seller  ? 

6.  What  does  the  receipt  show  ? 

The  teacher  should  encourage  the  pupils  to  make  out  bills  of  goods 
at  prices  current  in  the  place  where  they  live.  The  meaning  of  the 
term  "debtor"  and  the  abbreviation  "Dr."  should  be  explained. 


BILLS  AND  RECEIPTS 
WRITTEN  EXERCISE 


261 


Copy,  fill,  foot,  and  receipt  each  of  the  following  hills, 
dating  it  and  the  receipt  at  the  place  where  you  live,  and 
signing  your  name  as  the  clerk  who  received  the  money : 


1. 


Air.  Robert  Lee 


Bought  of  GEORGE  HALL 


*        Jan. 


9  doz.  eggs 
9  lb.  butter 
6  lb.  cheese 


@  32  f^ 


Mr.  James  Keene 


Received  Payment 

^&o.    fi-a.ll 

2. 

Bought  of  B.  S.  OSBORNE  &  CO 


Oct. 


12  yd.  silk 
9  yd.  lace 
8  yd.  ribbon 


Mr.  R.  S.  Bell 


@  fl.OO 

@  sop 


Bought  of  McCLINTOCK  &  CO. 


Apr. 


May 


6 
15 
10 


3  yd.  silk 
2  doz.  buttons 
12  yd.  calico 
5  yd.  lace 
9  yd.  linen 
2  yd.  ribbon 


@  80f^ 
@  45  fK 
@  7'/ 
@  40  ff 
@  60/ 
@   75/ 


262  BILLS  AND  RECEIPTS 

Copy,  fXl,  foot,  and  reoeipt  the  following,  as  on  page  261: 

4. 

[Name  of  place,  and  date'] 19 

M IName] 

Bought  of [Name] ,  Dealer  in  Meats  and  Poultry 


....iDate].. 


6  lb.  roast  beef 
6  lb.  chicken 

[BeceipC].. 


@   34ff 
@  £5/ 


5. 

[Name  of  place,  and  date] 19. 


M [Name].. 


Bought  of [Insert  name  of  some  grocer] ,  GrOCer 


.[Date].. 


4  lb.  powdered  sugar 
3  doz.  eggs 
^  doz.  oranges 

[Receipt] 


@   7/ 
@   60^ 


[Name  of  place,  and  date] 19., 


M [Name].. 


Bought  of. 


.[iVrtmc] ,  Grocer 


[Date] 

2  heads  lettuce 

@    5/ 

$ 

(( 

6  lb.  butter 

@.  32/ 

(( 

4  gal.  oil 

@   18/ 

ti 

8  lb.  raisins 

@  13/ 

u 

3  lb.  coffee 

[Seceipf] 

@  30/ 

$ 

BILLS  OF  GOODS  263 

WRITTEN  EXERCISE 

Make  out  hills  for  the  following : 

1.  15  lb.  gramilated  sugar  @  5^,  3  pk.  fancy  potatoes 
@  25^,  4  cans  salmon  @  8^. 

2.  7  lb.  butterine  @  25^,  4  jars  New  Orleans  molasses 
@  20^,  2  packages  raisins  @  9^,  5  boxes  matches  @  4^. 

3.  84  gro.  bone  buttons  @  18^,  694  yd.  cambric  @  17^, 
72  doz.  pearl  buttons  @  9^,  364  yd.  cashmere  @  82^. 

12  dozen  =  1  gross  (gro.).    Therefore  144  =  1  gro. 

4.  8  doz.  combs  @  |1.95,  4  doz.  brushes  @  $18.37,  3  doz. 
atomizers  @  $19.25,  4  gro.  toothbrushes  @  $9.35,  J  gro. 
nailbrushes  @  $27.50. 

5.  480  yd.  matting  @  18 (^,  375  yd.  matting  @  19  (^, 
284  yd.  carpet  @  48 (^,  8  rugs  @  $7.33,  4  doz.  doormats 
@  $6.75. 

6.  9  dining-room  sets  @  $62.50,  16  rockers  @  $5.35, 
8  sideboards  @  $32.50,  6  card  tables  @  $8.75,  4  china  closets 
@  $17.50. 

7.  325  yd.  carpet  @  48^,  520  yd.  matting  @  22^,  16  rugs 
@  $6.40,  4  rugs  @  $12.50, 3  doz.  doormats  @  $7.30, 328  yd. 
calico  @  6^. 

8.  8  doz.  hatchets  @  $10.75,  6  doz.  pairs  hinges  @  $4.35, 

5  doz.  carpenter's  squares  @  $34.50,  ^  gro.  locks  @  $42.50, 
8  doz.  files  @  $6.25. 

9.  75  M  (75,000)  envelopes  @  $2.30,  75  lb.  paper  @  22 (^, 
4  doz.  fountain  pens  @  $23.50,  10  doz.  bottles  ink  @  42^, 

6  dictionaries  @  $5.50. 


264  GENERAL  REVIEW 

XI.    GENERAL  REVIEW 
WRITTEN  EXERCISE 

1.  Frank's  father  had  $1250  in  a  bank.  He  drew  out 
$533  and  afterwards  $265.  How  many  dollars  did  he  still 
have  in  the  bank  ? 

2.  Charles  has  250  chickens.  In  one  yard  he  has  46 
chickens ;  in  another,  35 ;  and  in  another,  53.  How  many 
chickens  has  he  that  are  not  in  these  yards  ? 

3.  Mary  bought  8  yd.  of  cloth  at  5  ^  a  yard.  How  much 
change  should  she  receive  if  she  gave  the  storekeeper  a 
half  dollar? 

4.  If  62  acres  of  land  cost  $992,  how  much  will  1  acre 
cost  ?   How  much  will  40  acres  cost  ? 

5.  One  house  is  valued  at  $7270  and  another  house  at 
three  times  as  much.    How  much  are  both  together  worth  ? 

6.  If  6  overcoats  cost  $144,  how  many  overcoats  can  be 
bought  for  $1320  ?   (First  find  the  cost  of  one  overcoat.) 

7.  Mr.  Jackson  had  $700.  How  much  money  mil  he 
have  left  after  buying  a  horse  for  $150,  a  wagon  for  $45, 
and  4  cows  at  $35  each  ? 

8.  What  is  the  cost  of  15  yd.  of  velvet  at  $1.25  a  yard 
and  5  yd.  of  ribbon  at  37^  a  yard  ? 

9.  I  have  63  bu.  of  corn  in  one  bin,  54  bu.  in  another, 
37  bu.  in  a  third,  and  29  bu.  in  a  fourth.  How  many  pecks 
of  com  do  I  have  ? 

Teachers  will  observe  that  the  problems  in  this  exercise  are  two-step 
problems.   This  type  of  problem  has  been  approached  gradually. 


PROBLEMS  265 

10.  What  is  the  cost  of  16  barrels  of  flour  at  $6.25  a 
barrel  and  7 barrels  of  apples  at  |2.50  a  barrel? 

11.  From  a  bin  containing  516  bu.  of  oats,  65  bu.  were 
sown  and  73  bn.  have  been  fed  to  horses.  How  many 
bushels  of  oats  are  left? 

12.  What  is  the  cost  of  fencing  a  park  36  rd.  long  and 
14  rd.  wide  at  $2.50  a  rod  ? 

13.  If  a  man  having  $1000  buys  5  horses  at  $152  each 
and  spends  the  rest  of  his  money  for  cows  at  $40  apiece, 
how  many  cows  does  he  buy  ? 

Take  5  x  $152  from  $1000,  and  then  divide  by  $40. 

14.  At  a  rent  of  $23  a  month  for  a  house  and  $12  a 
month  for  a  stable,  what  is  the  rent  of  both  for  1  yr.? 

15.  What  is  the  cost  of  9  horses  at  $175.75  each  and 
76  tons  of  hay  at  $18.50  a  ton? 

16.  Find  the  area  of  a  field  40  rd.  long  and  24  rd.  wide. 
Draw  a  plan  of  the  field  on  the  scale  of  J  in.  to  4  yd. 

17.  A  mile  of  gas  pipe  is  laid  at  a  cost  of  $5  a  rod. 
What  is  the  cost  of  laying  the  pipe? 

18.  At  40^  a  dozen,  what  will  30  lemons  cost  ? 

19.  How  many  yards  of  braid  will  be  required  to  bind  a 
rug  5  ft.  long  and  3  ft.  wide  ? 

20.  If  a  man  travels  70  mi.  a  day,  how  many  days  will 
it  take  him  to  make  a  trip  of  1470  mi.  ? 

Find  how  many  times  70  is  contained  in  1470. 

21.  At  $40  an  acre,  what  will  2  eighty-acre  farms  cost  ? 

22.  How  many  Quarts  in  248  pt.?   How  many  gallons? 


266  GENERAL  REVIEW 

23.  A  milk  dealer  sells  every  day  16  cans  of  milk,  each 
holding  2  gal.   How  many  quarts  does  he  sell  ? 

24.  A  grocer  bought  4  bu.  of  apples  at  80^  a  bushel  and 
sold  them  at  25^  a  peck.    How  much  did  he  gain? 

25.  What  is  the  price  of  a  dozen  oranges  at  the  rate  of 

3  oranges  for  a  dime? 

26.  A  man  earns  35^  an  hour  and  works  2  da.  of  8  hr. 
each.    How  much  does  he  receive  ? 

27.  At  20^  a  square  yard,  what  will  it  cost  to  oil  a  floor 
6  yd.  long  and  4  yd.  wide  ? 

28.  Draw  a  plan  of  the  floor  in  Ex.  27  on  the  scale  of 
^  in.  to  1  yd.    Find  the  perimeter  of  the  room. 

29.  A  carload  of  coal  containing  30,000  lb.  was  sold  at 
|6  a  ton.   How  much  was  received  ? 

30.  How  many  cubic  feet  of  stone  in  a  wall  20  ft.  long, 

4  ft.  high,  and  2  ft.  thick? 

31.  Walter  has  100  inch  cubes.  They  are  built  into  a 
sohd  10  in.  long  and  2  in.  wide.   How  high  is  the  sohd? 

32.  How  many  pint  packages  can  a  seedsman  fill  from 
2  pk.  2  qt.  of  seeds  ? 

33.  If  a  man  earns  $2  a  day,  how  many  days  will  it  take 
him  to  earn  $24  ?  to  earn  $36  ?  to  earn  $96  ? 

34.  A  boy  bought  4  doz.  pencils  at  35^  a  dozen  and  sold 
them  at  4(^  apiece.    How  much  did  he  gain  ? 

35.  A  peddler  in  a  city  buys  a  pushcart  for  $22.  He  has 
$14.75  of  his  own  and  borrows  $3.50  from  his  brother. 
How  much  more  does  he  borrow  to  buy  the  pushcart? 


PEOBLEMS  267 

36.  A  peddler  bought  6  doz.  oranges  at  15^  a  dozen 
and  sold  them  at  2^  apiece.  How  much  did  he  make  on 
all  the  oranges? 

37.  A  man  bought  4  bunches  of  bananas.  The  first 
bunch  contained  120  bananas;  the  second,  176;  the  third, 
160;  and  the  fom*th,  240.  He  sold  the  bananas  at  the 
rate  of  4  for  5^.    How  much  did  he  receive  for  them? 

38.  A  workman  in  a  factory  makes  9  doz.  caps  a  day. 
How  many  caps  can  he  make  in  the  6  working  days  of  a 
week  ?   How  many  can  he  make  in  7  wk.? 

39.  If  a  workman  uses  2  buttons  on  each  cap  that  he 
makes,  how  many  caps  can  be  trimmed  with  12  doz. 
buttons?  How  many  can  be  trimmed  with  24  doz.  buttons? 

40.  A  newsboy  pays  3^  for  5  newspapers.  How  much 
money  must  he  have  in  order  to  buy  75  newspapers  ? 

41.  A  grocer  sells  8  eggs  marked  36^  a  dozen.  How 
much  change  should  he  give  for  25^? 

42.  A  boy  runs  on  errands  for  a  grocer.  He  gets  his 
car  fare  and  also  5(^  for  each  errand.  How  much  does  he 
get  if  he  runs  on  9  errands  and  pays  20^  for  car  fare  ? 

43.  A  workman's  wages  are  $2.50  a  day,  and  he  usually 
works  6  da.  each  week.  This  week  he  stays  at  home  2  da. 
How  much  will  he  find  in  his  pay  envelope  at  the  end  of 
the  week  ? 

44.  Our  class  has  28  children.  The  teacher  and  the  chil- 
dren go  on  a  picnic  and  pay  10^  each  for  car  fare.  They 
have  $8.75  for  the  picnic.  How  much  money  is  left  for 
luncheon  after  paying  all  the  car  fares? 


268  GENERAL  EEVIEW 

PROBLEMS  WITHOUT  NUMBERS 

1.  If  you  know  the  cost  of  each  of  two  different  things, 
how  do  you  find  the  cost  of  both  together  ? 

2.  If  you  know  the  number  of  feet  in  a  piece  of  string, 
and  cut  off  a  part  of  the  string,  how  do  you  find  the  length 
of  what  is  left  ? 

3.  If  you  know  the  cost  of  one  yard  of  cloth,  how  do 
you  find  the  cost  of  a  given  number  of  yards  ? 

4.  If  you  have  a  certain  number  of  inches  of  cloth  of  a 
certain  width,  and  a  book  cover  requires  a  certain  number 
of  inches  of  this  width,  how  do  you  find  the  number  of 
books  you  can  cover  with  all  the  cloth? 

5.  If  you  know  the  number  of  quarts  of  milk  in  a  can, 
how  do  you  find  the  number  of  pints  ? 

6.  If  you  know  the  length  of  a  piece  of  picture  molding 
in  feet,  how  do  you  find  the  length  in  inches  ? 

7.  How  do  you  multiply  a  number  of  two  figures  by  a 
number  of  one  figure  ? 

8.  What  do  you  mean  by  drawing  a  line  to  a  given 
scale,  say,  to  the  scale  of  1  in.  to  a  foot  ? 

9.  How  do  you  draw  a  rectangle  to  a  given  scale  ? 

10.  How  do  you  find  the  area  of  a  rectangle  ?   Draw  a 
rectangle  to  explain  your  answer. 

11.  Draw  this  page  of  the  book  to  some  scale,  and  write 
below  the  plan  the  scale  that  you  have  used. 

12.  Draw  a  plan  of  the  top  of  your  desk  to  some  scale, 
and  write  below  the  plan  the  scale  that  you  have  used. 


USING  WHAT  YOU  HAVE  LEARNED  269 

XII.  USING  WHAT  YOU  HAVE  LEARNED 
THE  SURPRISE  PARTY 

1.  Fanny  will  be  9  years  old  next  week,  and  the  class 
is  going  to  give  her  a  surprise  party.  There  are  17  boys 
and  19  girls  besides  Fanny.  The  boys  agree  to  put  in  15^ 
apiece  and  the  girls  10^  apiece.  How  much  will  the  boys 
put  in  ?  How  much  will  the  girls  put  in  ? 

2.  How  much  money  will  the  boys  and  girls  put  in  for 
Fanny's  surprise  party  in  Ex.  1  ? 

3.  They  take  out  75^  for  flowers.   How  much  does  that 

leave  ? 

4.  With  what  is  left,  after  taking  out  the  money  for  the 
flowers,  they  think  of  bujdng  a  present  for  Fanny.  They 
spend  some  of  it,  however,  for  candles  for  the  cake,  and 
have  $3.50  left.   How  much  did  they  spend  for  candles  ? 

5.  They  priced  a  watch  and  found  that  this  would  use 
half  of  the  |3.50.  What  was  the  price  of  the  watch?  If 
they  buy  it,  how  much  money  will  they  have  left  ? 

6.  They  bought  the  watch  and  then  bought  a  silver 
bracelet  for  $1.50,  and  decided  to  give  the  rest  to  a  poor 
woman  whom  Fanny  liked.  How  much  money  did  they 
give  to  the  woman? 

7.  At  the  night  of  the  party  each  of  the  19  girls  took 
4  little  cakes  to  the  party.   How  many  did  they  all  take  ? 

8.  Since  the  boys  wanted  to  do  their  share,  each  one  took 
6  apples.  How  many  apples  did  the  17  boys  take  ? 


270 


USING  WHAT  YOU  HAVE  LEARNED 


CAMP  FIRE  GIRLS 

1.  Camp  Fire  Girls  are  over  12  yr.  old.  In  how  many 
years  and  months,  to  the  nearest  month,  will  each  girl  in 
your  class  be  old  enough  to  be  a  member  ? 

2.  A  group  of  girls,  not  less  than  six  nor  more  than 
twenty  in  number,  can  form  a  Camp  Fire.  In  a  certain 
town  there  are  7  Camp  Fires,  averaging  14  girls  each. 
How  many  Camp  Fire  Girls  are  there  in  the  town? 

3.  A  Camp  Fire  of  14  girls  found  that  they  could  buy 
their  gowns  for  $2.50  each,  or  could  buy  the  materials  for 
$1.70  each.  How  much  would  they  save  in  all  by  buying 
the  materials  and  making  their  gowns? 

4.  There  are  three,  ranks  of  Camp  Fire  Girls,  the  Wood 
Gatherer,  the  Fire  Maker,  and  the  Torch  Bearer.  In  our 
camp  there  are  7  Wood  Gatherers,  each  paying  $1.70  for 
the  materials  for  a  gown.   How  much  do  the  seven  pay  ? 


CAMP  FIRE  GIRLS  271 

5.  There  were  4  Fire  Makers  in  the  camp.  Each  paid 
$1.50  for  a  Fire  Maker's  bracelet,  $1.70  for  materials  for 
a  gown,  and  $1.25  for  a  pair  of  moccasins.  How  much  did 
each  Fire  Maker  pay  in  all  ?   How  much  did  all  four  pay  ? 

6.  There  were  3  Torch  Bearers  in  the  camp.  Each  paid 
$1.50  for  a  Torch  Bearer's  pin,  25^  for  a  Camp  Fire  hat- 
pin, 65^  for  materials  for  bloomers,  30^  for  a  dozen  Camp 
Fire  buttons,  and  25^  for  a  Torch  Bearer's  emblem.  How 
much  did  each  pay  in  all  ?   How  much  did  all  three  pay  ? 

7.  The  Camp  Fire  Girls  have  many  honors.  For  Home 
Craft  Honors  a  girl  must  do  things  about  the  house. 
Among  other  things  she  must  plan  refreshments  for  a 
party  of  10  girls,  not  spending  more  than  $1.  Make  such 
a  plan  and  bring  the  list,  with  prices,  to  school  to-morrow. 

8.  For  Hand  Craft  Honors  a  girl  must  do  things  with 
her  hands,  such  as  make  a  skirt.  Find  out  how  much  the 
materials  for  a  school  skirt  would  cost,  and  bring  the  list, 
with  prices,  to  school  to-morrow. 

9.  The  Camp  Fire  Girls  often  go  out  to  camp.  Eight  of 
them,  besides  the  Guardian  of  the  Fire  (making  nine  in 
all),  went  camping.  They  spent  40^  each  for  trolley  fares, 
$1.60  each  for  railway  tickets,  $5.40  for  the  rent  and  car- 
riage of  the  tents  for  the  party,  and  $24.44  for  food  and 
camp  expenses  for  the  party.  How  much  did  they  spend 
in  all  ?  How  much  should  each  contribute  if  the  Guardian 
of  the  Fire  had  her  expenses  paid  by  the  rest  of  the  girls  ? 

To  many  girls  this  subject  of  the  Camp  Fire  Girls  is  of  great  interest. 
For  such  pupils  these  two  pages  are  especially  intended.  Through  the  kind- 
ness of  the  national  organization  the  illustration  on  page  270  is  printed. 


272  LITTLE  EXAMINATION'S 

XIII.   LITTLE  EXAMINATIONS 

I.   1.  4856  +  9237.  6.  300  x  $1.75. 

2.  7902  -  5919.  7.  72  x  $3.75. 

3.  $40.73  +  $20.96.  8.  475  x  582. 

4.  $50.13  -  $32.75.  9.  25,984  -^  58. 

5.  7  X  $2.96.  10.  2  cu.  ft.  =  (?)  cu.  in. 

n.   1.  8346  +  9078.  6.  400  x  $2.40. 

2.  3709  -  2963.  7.  38  x  $4.22. 

3.  $30.82  +  $52.86.  8.  287  x  496. 

4.  $52.32 -$29.56.  9.  7500^-125. 

5.  8  X  $2.85.  10.  4  cu.  ft.  =  (?)  cu.  in. 

m.   1.  4283  +  6296.  7.  68  x  $5.37. 

2.  4132  -  2876.  8.  394  x  498. 

3.  $40.27 +  $32.96.  9.  14,500-^125. 

4.  $60.01 -$19.83.  10.  288  sq. in.  =  (?)  sq.ft. 

5.  9  X  $3.27.  11.  17bu.  =  (?)pk. 

6.  520  X  $3.04.  12.  I  of  64. 

IV.   1.  7129  +  3786.  7.  49  x  $7.72. 

.       2.  5235  -  2868.  8.  778  x  642. 

3.  $23.49  +  $87.62.  9.38,802^116. 

4.  $52.29  -  $26.60.  10.  9  sq.  ft.  =  (?)  sq.  in. 

5.  6  X  $4.72.  11.  40  pt.  =  (?)  qt. 

6.  760  X  $4.60.  12.  f  of  96. 

Teachers  should  read  the  note  on  page  52. 


WHAT  THE  PUPIL  SHOULD  KNOW  273 

XIV.  WHAT  THE  PUPIL  SHOULD  KNOW  WHEN  HE 
HAS  FINISHED  THIS  BOOK 

YOU  SHOULD  ADD  QUICKLY  AND  ACCURATELY 

Copy  and  add,  timing  yourself  on  each  set  often  examples. 

1.  4136  +  9287.  21.  $52.43  +  $48.76. 

2.  3092  +  4768.  22.  $524.30  +  $48.76. 

3.  4381  +  8092.  23.  5243  +  4876. 

4.  5276  +  8397.  24.  8179  +  9283. 

5.  4855  +  8762.  25.  $81.79  +  $92.83. 

6.  3984  +  9876.  26.  $817.90  +  $928.30. 

7.  8237  +  4583.  27.  $54.62  +  $87.96. 

8.  5692  +  8173.  28.  $78.37  +  $49.87. 

9.  8494  +  9877.  29.  $70.36  +  $89.09. 

10.  4086  +  3790.  30.  $37.49  +  $98.97. 

11.  6842  +  9382.  31.  428  +  396  +  987. 

12.  7209  +  9089.  32.  629  +  438  +  909. 

13.  8778  +  8296.  33.  778  +  896  +  408. 

14.  4009  +  8999.  34.  539  +  683  +  997. 

15.  6872  +  1983.  35.  $5.28  +  $4.96  +  $3.74. 

16.  4849  +  2183.  36.  $52.80  +  $4.96  +  $37.40. 

17.  7680  +  9398.  37.  $52.80  +  $4.96  +  $3.74. 

18.  4777  +  8643.  38.  $128.90  +  $34.76  +  $48.23. 

19.  5273  +  8556.  39.  $12.89  +  $34.76  +  $48.23. 

20.  4196  +  3784.  40.  $12.89  +  $347.60  +  $428.30. 

Efficiency  tests  of  this  kind  are  helpful  throughout  the  course,  and  many 
of  them  are  provided  in  this  book. 


274  WHAT  THE  PUPIL  SHOULD  KNOW 

YOU  SHOULD  SUBTRACT  QUICKLY  AND  ACCURATELY 

Copy  and  subtract,  timing  yourself  on  each  set  of  ten 
examples :    ^j 

1.  7830 -fBm^.  21.  $29.60-13.48. 

2.  8lfcVf3894r  22.  $128.30  -  $26.37. 

3.  6209-4836.  23.  $201.40  -  $52.33. 

4.  7108-2987.  24.  $280.30  -  $29.46. 

5.  5633-1987.  25.  $310.02  -  $38.36. 

6.  4206  -  1899.  26.  $401.01  -  $56.75. 

7.  3837  -  1968.  27.  $126.37  -  $109.48. 

8.  9001-2983.  28.  $630.02  -  $427.63. 

9.  8002-3093.  29.  $702.23  -  $426.48. 

10.  6277-4968.  30.  $523.41  -  $239.68. 

11.  5307-2836.  31.  $429.83  -  $327.60. 

12.  6612-4833.  32.  $527.75  -  $209.09. 

13.  4702-3685.  33.  $607.07  -  $421.36. 

14.  6211  -  2033.  34.  $528.28  -  $492.99. 

15.  4787-2939.  35.  $800.70  -  $528.36. 

16.  2192-1998.  36.  $602.73  -  $478.64. 

17.  6070-3841.  37.  $281.32  -  $193.82. 

18.  5791  -  2992.  38.  $1026.00  -  $873.75. 

19.  6280-5691.  39.  $2000.00  -  $1482.60. 

20.  2936-1987.  40.  $2172.30  -  $1986.45. 

In  computing  the  time,  the  pupil  should  include  the  time  of  copying. 
In  practical  business  we  have  to  write  the  numbers  as  well  as  subtract 
them,  and  this  is  part  of  the  training.  The  pupil  should  learn  to  write 
the  numbers  neatly  and  accurately  as  well  as  quickly. 


EFFICIENCY  TESTS  275 

YOU  SHOULD  MULTIPLY  QUICKLY  AND  ACCURATELY 

Copy  and  multiply,  timing  yourself  on  each  set  of  ten 
examples : 

1.  29  X  38.  21.  121  X  342.  41.  2  x  |48.72. 

2.  42  X  70.  22.  426  x  809.  42.  3  x  $96.80. 

3.  63  X  96.  23.  707  x  556.  43.  5  x  $40.75. 

4.  45  X  84.  24.  432  x  487.  44.  7  x  $36.42. 

5.  32  X  29.  25.  562  x  809.  45.  4  x  $80.92. 

6.  86  X  98.  26.  977  x  844.  46.  9  x  $78.82. 

7.  70  X  93.  27.  555  x  876.  47.  6  x  $68.08. 

8.  80  X  90.  28.  743  X  201.  48.  7  x  $98.74. 

9.  68  X  86.  29.  529  x  826.  49.  9  x  $56.43. 

10.  44  X  88.  30.  432  x  481.  50.  8  x  $80.96. 

11.  14  X  236.  31.  26  X  3478.  51.  15  x  $2.78. 

12.  43  X  309.  32.  43  x  8296.  52.  28  x  $3.46. 

13.  57  X  877.  33.  21  x  8477.  53.  56  x  $4.09. 

14.  92  X  379.  34.  30  x  9872.  54.  42  x  $9.81. 

15.  64  X  909.  35.  62  x  890T.  55.  77  x  $8.75. 

16.  83  X  888.  36.  48  x  7460.  56.  48  x  $21.36. 

17.  47  X  926.  37.  38  x  9080.  57.  37  x  $92.08. 

18.  35  X  875.  38.  65  x  2178.  58.  56  x  $90.09. 

19.  44  X  557.  39.  36  x  8472.  59.  78  x  $89.86. 

20.  63  X  892.  40.  27  x  9628.  60.  96  x  $86.79. 


In  giving  such  efficiency  tests  the  teacher  may  find  it  of  advantage  to 
give  on  one  day  Exs.  1-10  on  page  273,  Exs.  1-10  on  page  274,  Exs.  1-10 
on  page  275,  and  so  on ;  and  on  another  day  Exs.  11-20  on  the  same  pages. 


276 


WHAT  THE  PUPIL  SHOULD  KNOW 


2. 

378- 

-24. 

3. 

626- 

-28. 

4. 

875- 

-43. 

6. 

920- 

-37. 

6. 

801- 

-49. 

7. 

676- 

-33. 

8. 

494- 

-19. 

9. 

962- 

-32. 

10. 

488- 

-27. 

11. 

1283 

^38. 

12. 

4072 

^56. 

13. 

5710 

^29. 

14. 

8209 

^37. 

15. 

9108 

^43. 

16. 

9807 

^46. 

17. 

5055 

^75. 

18. 

8026 

-^93. 

19. 

9071 

^85. 

20. 

9002 

-*-96. 

92. 
46. 


YOU  SHOULD  DIVIDE  QUICKLY  AND  ACCURATELY 

Copy  and  divide,  writing  both  quotient  and  remainder^ 
timing  yourself  on  each  set  of  ten  examples : 

1.  428  -  26.    21.  2173  ^  42.    41.  |144  -^  12. 

22.  5683^85. 

23.  8093-92. 

24.  9062^77. 

25.  8112 

26.  3984 

27.  5085-^-70. 

28.  3700-69. 

29.  4008-90. 

30.  7782-56. 

31.  5434-82. 

32.  4848-49. 

33.  6209-80. 

34.  5000-91. 

35.  3707-86. 

36.  5200-35. 

37.  4801-20. 

38.  8237-92. 

39.  5781 

40.  4000 

In  practical  work  in  division  there  is  usually  a  remainder.  When  the 
pupil  studies  a  more  advanced  book  he  can  carry  the  quotient  as  far  as  may 
be  necessary  by  means  of  decimal  fractions.  At  present  he  should  merely 
indicate  the  remainder  or  write  a  common  fraction  in  the  quotient. 


86. 
99. 


42.  $288-24. 

43.  $17.28-4. 

44.  $1728  -  12. 

45.  $1728  -  24. 

46.  $1331  -  11. 

47.  $7007  -^  11. 

48.  $2626-13. 

49.  $2756  -  13. 

50.  $4575-25. 

51.  $1270  -4- 12. 

52.  $3250-14. 

53.  $1236-21. 

54.  $2238-33. 

55.  $4756  -  42. 

56.  $4020  -  45. 

57.  $5005  -  72. 

58.  $6172-36. 

59.  $4856-29. 

60.  $3792  -  18. 


EFFICIENCY  TESTS 


277 


YOU  SHOULD  BE  ABLE  TO  REDUCE,  ADD,  AND  SUBTRACT 

THE  ORDINARY  COMMON  FRACTIONS  OF  BUSINESS,  AND 

FIND  A  FRACTIONAL  PART  OF  A  WHOLE  NUMBER 


Copy,  and  perform 
self  on  each  set  of  ten 


1. 

1=6- 

2. 

1=8. 

3. 

4  =  ?- 

4. 

8        16- 

5. 

l  =  T6-- 

6. 

i  =  ^- 

7. 

4  =  ^- 

8. 

*  =  ?• 

d. 

i^TF- 

10. 

i^si- 

11. 

i  +  l- 

12. 

f  +  4- 

13.  }  +  i 

14.1  +  4 

15.  ^  +  1 

16.  4  +  4 

17     2.    I    1 

18.  l  +  i 

19.  I  +  J 

20.  1  +  4 


the 

operations 

exa' 

mples : 

21. 

1-1 
2      4- 

22. 

3._  1 
4         2' 

23. 

i-f 

24. 

i-l- 

25. 

l-f 

26. 

i-l 

27. 

F""  2- 

28. 

3.—  1 
5         3- 

29. 

2._1 

3         2- 

30. 

I-l- 

31. 

J  +  i  +  f 

32. 

h+l+h 

33. 

1+5.4-5 

2  ^  4  ^  8- 

34. 

i  +  i  +  f 

35. 

i  +  i  +  i- 

36. 

l  +  i  +  l- 

37. 

f+i+f 

38. 

i  +  i+i- 

39. 

f  +  i  +  i- 

40. 

*  +  *  +  !■ 

indicated,  timing  your- 


41. 
42. 
43. 
44. 
45. 
46. 
47. 
48. 
49. 
50. 
51. 
52. 
53. 
54. 
55. 
56. 
57. 
58. 
59. 
60. 


1  of  428. 
1  of  828. 
I  of  624. 
1  of  624. 
f  of  736. 
1  of  968. 
f  of  256. 
f  of  496. 
I  of  584. 
I  of  475. 

^+^• 

3i-2i. 
4f  +  3J. 


4^ 

^8 


^1 


6f  +  21 
61-24- 
4f+14- 

41-14- 

n + 24. 


278              WHAT  THE  PUPIL  SHOULD  KNOW 
THE  COMMON  TABLES  OF  MEASURES,  AND  HOW  TO  USE  THEM 

Copy,  and  complete  each  statement,  timing  yourself  on 
each  set  of  ten  examples : 

1.  1ft.  =  (?)in.  21.  llb.  =  (?)oz. 

2.  7  ft.  =  (?)  in.  22.  |  lb.  =  (?)  oz. 

3.  9  ft.  =  (?)  in.  23.  21  lb.  =  (?)  oz. 

4.  1yd.  =  (?)ft.  24.  16oz.  =  (?)lb. 

5.  7  yd.  =  (?)  ft.  25.  144  oz.  =  (?)  lb. 

6.  31  yd.  =  (?)  ft:  26.  288  oz.  =  (?)  lb. 

7.  1yd.  =  (?)in.  27.  1  T.  =  (?)  lb. 

8.  2iyd.  =  (?)in.  28.  SJ  T.  =  (?)  lb. 

9.  1  rd.  =  (?)  ft.  29.  1  qt.  =  (?)  pt. 

10.  2  rd.  =  (?)  ft.  30.  71  qt.  =  (?)  pt. 

11.  Ird.  =  (?)yd.  31.  1  gal.  =  (?)  qt. 

12.  9  rd.  =  (?)  yd.  32.  3|  gal.  =  (?)  qt. 

13.  1  mi.  =  (?)  rd.  33.  4|  gal.  =  (?)  pt. 

14.  4  mi.  =  (?)  rd.  34.  1  bu.  =  (?)  pk. 

15.  1  mi.  =  (?)  yd.  35.  71  bu.  =  (?)  pk. 

16.  J  mi.  =  (?)  yd.  36.  1  pk.  =  (?)  qt. 

17.  1  mi.  =  (?)  ft.  37.  51  pk.  =  (?)  qt.       . 

18.  31  mi.  =  (?)  ft.  38.  7  sq.  ft.  =  (?)  sq.  in. 

19.  I  mi.  =  (?)  ft.  39.  7  sq.  yd.  =  (?)  sq.  ft. 

20.  i  mi.  =  (?)  ft.  40.  7  hr.  =  (?)  min. 

Teachers  should  remember  that  we  no  longer  use  such  numbers  as  4  mi. 
17  rd.  3  yd.  2  ft.  2  in. 


TABLES  FOR  REFERENCE  279 

Length 
12  inches  (in.)  =  1  foot  (ft.) 
3  feet  =  1  yard  (yd.) 
161  feet  =  1  rod  (rd.) 
5280  feet,  or  320  rods  =  1  mile  (mi.) 

Square  Measure 
144  square  inches  (sq.  in.)  =  1  square  foot  (sq.  ft.) 
9  square  feet  =  1  square  yard  (sq.  yd.) 
30J  square  yards  =  1  square  rod  (sq.  rd.) 
160  square  rods  =  1  acre  (A.) 

640  acres  =  1  square  mile  (sq.  mi.) 

Cubic  Measure 
1728  cubic  inches  (cu.  in.)  =  1  cubic  foot  (cu.  ft.) 
27  cubic  feet  =  1  cubic  yard  (cu.  yd.) 
128  cubic  feet  =  1  cord  (cd.) 

Weight 
16  ounces  (oz.)  =  1  pound  (lb.) 
2000  pounds  =  1  ton  (T.) 

Liquid  Measure 

4  gills  (gi.)  =  1  pint  (pt.) 
2  pints  =  1  quart  (qt.) 
4  quarts  =  1  gallon  (gal.) 

Dry  Measure 
2  pints  (pt.)  =  1  quart  (qt.) 
8  quarts  =  1  peck  (pk.) 
4  pecks  =  1  bushel  (bu.) 


280 


TABLES  rOR  REFERENCE 


Multiplication  Table 


1 

x2  = 

=   2 

2 

x2  = 

=   4 

3 

x2  = 

=    6 

4 

x2  = 

:       8 

5 

x2  = 

=  10 

6 

x2  = 

=  12 

7 

x2  = 

=  14 

8 

x2  = 

=  16 

9 

x2  = 

=  18 

10 

x2  = 

=  20 

11 

x2  = 

=  22 

12 

x2  = 

=  24 

1 

x3  = 

=   3 

2 

x3  = 

=   G 

3 

x3  = 

=   9 

4 

x3  = 

=  12 

5 

x3  = 

=  15 

6 

x3  = 

=  18 

7 

x3  = 

=  21 

8 

x3  = 

=  24 

9 

x3  = 

=  27 

10 

x3  = 

=  30 

11 

x3  = 

=  33 

12 

x3  = 

=  36 

1x4  = 

=   4 

2x4  = 

=   8 

3x4  = 

=  12 

4x4  = 

=  16 

5x4  = 

=  20 

6x4  = 

=  24 

7x4  = 

=  28 

8x4  = 

=  32 

9x4  = 

=  36 

10x4  = 

=  40 

11x4  = 

=  44 

12x4  = 

=  48 

1 

X  5  = 

=   5 

2 

x5  = 

=  10 

3 

x5  = 

=  15 

4 

x5  = 

=  20 

5 

x5  = 

=  25 

6 

x5  = 

=  30 

7x5  = 

=  35 

8 

x5  = 

=  40 

9 

x5  = 

=  45 

10 

x5  = 

=  50 

11 

x5  = 

=  55 

12 

x5  = 

=  60 

1 

x6  = 

=   6 

2 

x6  = 

=  12 

3 

x6  = 

=  18 

4 

x6  = 

=  24 

5 

x6  = 

=  30 

6 

x6  = 

=  36 

7 

x6  = 

=  42 

8 

x6  = 

=  48 

9 

x6  = 

=  54 

10 

x6  = 

=  60 

11 

x6  = 

=  66 

12 

x6  = 

=  72 

1x7  = 

=   7 

2x7  = 

=  14 

3x7  = 

=  21 

4x7  = 

=  28 

5x7  = 

=  35 

6x7  = 

=  42 

7x7  = 

=  49 

8x7  = 

=  56 

9x7  = 

=  63 

10x7  = 

=  70 

11x7  = 

=  77 

12x7  = 

=  84 

1x8  = 

=   8 

2x8  = 

=  16 

3x8  = 

=  24 

4x8  = 

=  32 

5x8  = 

=  40 

6x8  = 

=  48 

7x8  = 

=  56 

8x8  = 

=  64 

9x8  = 

=  72 

10x8  = 

=  80 

11x8  = 

=  88 

12x8  = 

=  96 

1x9  = 

9 

2x9  = 

18 

3x9  = 

27 

4x9  = 

36 

5x9  = 

45 

6x9  = 

54 

7x9  = 

63 

8x9  = 

72 

9x9  = 

81 

10x9  = 

90 

11x9  = 

99 

12x9  = 

108 

INDEX 


PAGE 

Acute  triangle 240 

Addend 114 

Addition,  5,  20,  57,  114,  118,  169,  225 

check  on 28,  114 

deiined 114 

table 23 

Aliquot  part 259 

Area 151 

Average 191,  199 

Bills 110,  260 

Birthday  party 164 

Boy  Scouts 246 

Buying  things  we  would  like  .    .    165 

Camp  Fire  Girls 270 

Cancel 252 

Change,  making 121,  171 

Check  on  addition 28,  114 

on  division 74,  188 

on  subtraction 32 

Christmas  problems 183 

City,  a  day  in  the 185 

City  boy  and  girl 145 

Counting 1,  15 

Country  boy  and  girl 104 

Cubic  measure 242 


PAGE 

Dividend 74,  188 

Division    ...      71,  93,  124,  187,  230 

check  on    .    .    ' 74,  188 

defined 74 

Divisor 74,  188 

Dramatization  explained     .    .    .  3,  6 

Dressing  the  dolls 91 

Drill  explained 27 

Drill  tests,  7,  24,  25,  27,  34,  35,  47, 
48,  57,  70,  88,  89, 107, 115, 143, 

144,  163,  169,  171,  186,  193 
Dry  measure 149 

Earning  money 116,  146 

Efficiency  tests 273 

Equals 5 

Exact  division 95 

Footing  a  bill ,    .    .    260 

Fractional  parts  .    .    .     101,  205,  251 
Fractions ...     38,  97,  147,  200,  248 

addition  of 202,  254 

reduction  of 252 

subtraction  of  ...    .    203,  257 

Games,  6,  9,  13,  26,  29,  31,  37,  91,  92 
General  review     .      102,  154,  218,  264 


Debtor 260      Hundreds 54 

Denominator 248 

Difference 65      Improper  fraction 248 

Dimensions 241      Integer 248 

281 


282 


INDEX 


PAGE 

Length 43,  233 

Liquid  measure 45,  213 

LittleExaminations,  52,108,166,222,272 

Long  division 191 

Lowest  terms 252 

Measures,  43,  45,  56, 149, 150, 151, 

213,  215,  233,  235,  242,  244,  245 

Millions 224 

Minuend 65 

Minus 11 

Mixed  number 248 

Money  .    .    16,  112,  118,  122,  172,  198 

Multiplicand 85,  172 

Multiplication  .     71,  85,  124,  172,  227 

defined 172 

tables 71,  124,  280 

Multiplier 85, 172 

Numbers  to  1000 53 

used  in  play 90 

Numerator 248 

Obtuse  triangle 240 

Perimeter 152 

Playing  store 3,  12,  37 

Plus 5 

Post  office 184 

Problems  about  our  class     ...      36 

about  our  store 37 

about  games 92 

■without  numbers  .    .    .    217,  268 

Product 85,  172 

Proper  fraction 248 

Quotient 74, 188 

Reading  and  writing  numbers,  53, 

109,  167,  223 


PAGE 

Receipt 260 

Receipting  a  bill 260 

Reduction  of  fractions     ....    252 

Remainder 65,  95 

Right  triangle 240 

Roman  numerals      .    .    .56,  111,  168 

Scale,  drawing  to     ....    151,  237 

Scout  camp 247 

Square  measure 151,  235 

Store  problems 37 

Subtraction  .    .    .10,  32,  64,  129, 

170,  226 

check  on 32 

defined 11 

methods  of 65 

Subtrahend ^  .    .    .      65 

Sum 5 

Surprise  party 269 

Tables  ....     23,  71,  124,  279,  280 

Taking  a  trip 220 

Terms  of  a  f  ra-ction 248 

Thousands 224 

Time 56,  215 

Triangle 240 

Troublesome  groups 25 

Unit 172 

of  measure 236 

United  States  money   ....  16, 112 
Using  what  you  have  learned,  36, 
49,  90,  104,  145, 164, 183,  220, 

246,  269 

Volume 242 

Weight 46,  150,  245 

What  the  pupil  should  know  .    .    273 
Wood  measure 244 


ANSWERS 

Page  54.  1.-555;  249;  121;  609;  303;  880.  2.  Two  hundred  forty^wo; 
two  hundred  seven ;  five  hundred  twenty ;  six  hundred  thirty-four ;  nine 
hundred  eighty-seven ;  eight  hundred  forty-three ;  seven  hundred  sixty-five. 

Page  55.  1.  101;  150.  2.  203;  270.  3.  306;  390.  4.  409;  540. 
5.  606;  708.  6.  Five  hundred  twenty-seven ;  six  hundred  forty-two ;  three 
hundred  thirty-four;  four  hundred  fifty-six;  six  hundred  seventy-eight; 
nine  hundred  nine ;  seven  hundred  forty-two ;  eight  hundred  thirty ;  three 
hundred  three.  7.  Seven  hundred  eight ;  eight  hundred  sixty ;  nine  hundred 
one;  seven  hundred  seventy-seven;  eight  hundred;  seven  hundred  fifty; 
six  hundred  thirty ;  four  hundred;  one  thousand.  8.  43;  877.  9.  21;  789. 
10.  52;  999.    11.  78;  678.    12.  500;  567.    13.  600;  673.    14.  700;  727. 

Page  58.  1.  70;  72;  77;  77;  77;  90.  2.  93;  99;  93;  99;  99;  80. 
3.  94;  94;  95;  98;  99;  100.  4.  360;  376;  379;  399 ;  599 ;  865.  5.  674; 
748;  789;  686;  859;  796. 

Page  60.  1.  60;  60;  61;  60;  64;  52;  90.  2.  60;  81;  92;  90;  80; 
62;    54.    3.  80;  52;  72;  63;  83;  45;  91.    4.  70;  73;  83;  46;  91;  51;  85. 

5.  75;  95;  68;  85;  74;  94;  92.  6.  85;  92;  90;  71;  83;  64;  65.  7.  77; 
81;  68;  80;  58;  73;  76.  8.  64;  81;  76;  82;  60;  81;  63.  9.  40;  54; 
60;  54;  74;  78;  83.     10.  72;  105;  107;  99;  100;  101;  85. 

Page  61.  1.  293.  2.  261.  3.  463  ft.  4.  382.  5.  575.  6.  574.  7.  760. 
8.  712.    9.  $554. 

Page  62.   1.  314.     2.  305  miles.     3.  405.     4.  625.      5.  54S.      6.  766. 

7.  652.     8.  |737. 

Page  63.    1.  352.    2.  656.    3.  642.    4.  417.    5.  680.    6.  833.    7.  710. 

8.  820.    9.  911.    10.  630.    11.  911.    12.  798.  13.  683. 

Page  66.  1,  25;  29;  44;  28;  28;  35;  58.  2.  28;  18;  27;  19;  28; 
43;  47.    3.  28;  16;  34;  18;  16;  34;  57.    4.  8;  27;  38;  29 ;  27;  43;  36. 

6.  1.5.    6.  14  ft.     7.  12.    8.  29  yr.    9.  14  in.    10.  3.    11.  17. 

EP  515.7  1 


2  ESSENTIALS  OF  ARITHMETIC 

Page  67.  1.  482;  473;  464;  482;  412;  211.  2.  292;  451;  282;  492; 
363;  467.    3.  272;  242;  252;  493;  185;  245. 

Page  69.  1.  526;  237;  334;  258;  236;  179.  2.  317;  469;  163;  179 
248;  235.  3.  219;  259;  146;  237;  289;  364.  4.  467;  225;  138;  355 
247;  508.  5.  577;  339;  589;  567;  387;  145.  6.  388;  587;  485;  434;  294 
346.    7.  109;  99;  199;  309;  498;  488.     8.  137.    9.  256.     10.  180  ft. 

Page  70.  1.  44.  2.  133.  3.  257.  4.  368.  5.  489.  6.  46.  7.  157. 
8.  269.  9.  338.  10.  421.  11.  252.  12.  267.  13.  378.  14.  449.  15.  558. 
16.  88.  17.  165.  18.  279.  19.  386.  20.  563.  21.  265.  22.  147.  23.  324. 
24.  235.    25.  36.    26.  97.    27.  88.    28.  177.    29.  189.    30.  276. 

Page  73.  1.  4;  8;  8;  12;  16;  18;  3;  18;  0;  0.  2.  6;;  6;  10;  10;  14; 
12;  2;  2;  14;  16. 

Page  76.  1.  3;  3;  0.  2.  3;  3;  8.  3.  3;  3;  6.  4.  3;  3;  12.  5.  $21; 
$27.    6.  $36;  $33. 

Page  77.  1.  3;  5;  8;  10.  2.  4;  6;  7;  9.  3.  7.  4.  4;  2.  5.  27;  21; 
18;  15;  24;  12. 

Page  78.    2.  3.    3.  2.    4.  3.    5.  2.    6.  3.    7.  4.    8.  6.    9.  4.    10.  3. 

Page  79.    1.  20;  28;  36.    2.  32.    3.  8;  28;  24;  32;  40.    4.  36;  28;  32. 

Page  80.    1.  28.    2.  36.    3.  12;  20;  32.    4.  28. 

Page  81.     1.  7;  9.    2.  6.    3.  6;  4 ;  10.    4.  8 ;  4 ;  9. 

Page  82.     1.  15.    2.  45f    3.  35.    4.  22;  33;  47.    5.  52;  29;  17. 

Page  83.  1.  5;  20;  3.  2.  5;  45;  8.  3.  9;  7;  5.  4.  7;  9;  3.  5.  8 ; 
10;  4.    6.  3. 

Page  84.    1.  6.    2.  3.    3.  6^.    4.  $27.    5.  8.    6.  $28. 

Page  85.  1.  26;  82;  84;  46;  48;  64;  644.  2.  63;  93;  88;  44;  28; 
69;  693. 

Page  87.  1.  212;  60;  308;  158;  264;  66;  666.  2.  192;  256;  65; 
171;  320;  48;  484.  3.  102;  220;  150;  24;  272;  160;  966.  4.  134;  294; 
3.52;  258;  306;  84;  844.    5.  267;  156;  168;  186;  388;  252;  924. 

Page  90.    1.  51.    2.  36.    3.  102.    4.  58.    5.  42.    6.  97. 

Page  91.    1.  85^.     2.  50^.     3.  36f     4.  40;    16;    4.     5.  8^.     6.  4^. 

7.  65^.    8.  192.    9.  60. 

Page  92.    1.  80f   2.  180  ft.  3.  360  ft.  4.  611.   5.  87.   6.  80.   7.  45f 

8.  36^.    9.  lOf 


ANSWERS  3 

Page  94.  1.  12;  14;  21;  24;  33;  41;  42;  422.  2.  11 ;  12 ;  20 ;  23; 
13;  32;  22;  222.  3.  11 ;  10 ;  20 ;  22 ;  21 ;  6  ;  12 ;  111.  4.  21.  5.  22. 
6.  12;  21;  30. 

Page  95.     1.  11,  rem.  2^.    2.  10,  rem.  3^.    3.  12,  rem.  If    4.  22,  rem.  1. 

5.  11,  rem.  2.  6.  22,  rem.  2.  7.  33,  rem.  1.  8.  11,  rem.  1.  9.  31,  rem.  1. 
10.  31,  rem.  1.  11.  21,  rem.  1.  12.  31,  rem.  2.  13.  40,  rem.  1.  14.32, 
rem.  1.    15.  22,  rem.  1. 

Page  96.  1.  16;  17;  26;  29;  36;  48;  22;  224.  2.  24 ;  8 ;  29 ;  18; 
16;  27;  21;  121.  3.  14  ;  13  ;  16  ;  18 ;  24 ;  23  ;  9  ;  91.  4.  13.  5.  30; 
28;  26;  19;  331.  6.  22;  21;  31;  19;  333.  7.  25.  8.  18. 

Page  97.  3.  2.  4.  3.  5.  6. 

Page  98.  1.  |.  2.  |,  or  1.  3.  0.  4.  i.  5.  2.  6.  3. 

Page  99.  1.  f  3.  8. 

Page  102.  1.  595;  655;  661;  779;  772;  587.  2.  881;  795;  935;  807 
875;  937.  3.  674;  864;  921;  855;  920;  920.  4.  642;  860;  784;  901 
760;  735.  5.  355;  295;  345;  285;  187;  198.  6.  2.59;  258;  404 
473;  592;  248.  7.  288;  307;  628;  157;  385;  513.  8.  376;  459;  389 
604;  295;  448.  9.  83;  78;  299;  54;  312;  414.  10.  50;  66;  28;  72 
90;  99.  11.  123;  92;  160;  128;  215;  135.  12.  110;  155;  126;  252 
120;  118.  13.  238;  308;  264;  400;  405;  228.  14.92.  15.  $72.  16.14 
23;  26;  11;  17;  29;  20;  8.  17.  19;  31;  35;  15;  23;  39;  27;  11.  18 
30;  34;  14;  22;  38;  26;  10.  18.  24  ;  39  ;  44  ;  19  ;  29  ;  49  ;  34  ;  14.  23 
38;  43;  18;  28;  48;  33;  13.  22 ;  37;  42 ;  17 ;  27;  47 ;  32;  12.  19.  16 
21 ;  26  ;  31 ;  36,  rem.  1 ;  37,  rem.  1.  20.  17  ;  19  ;  23  ;  25  ;  26,  rem.  2  ;  30 
rem.  1.  21.  12 ;  14  ;  18 ;  20,  rem.  1 ;  21,  rem.  3  ;  23,  rem.  1.  22.  13  ;  15 

14,  rem.  2  ;  16,  rem.  3  ;  19  ;  19,  rem.  4. 

Page  104.  1.  8.5.  2.  34.  3.  90 f  4.  75 f  5.  30.  6.  84  f  7.  37 f 
8.  Yes;  12 f    9.  70f     10.  80f    11.  $1.00.     12.  42f     13.  52f     14.  48f 

15.  $17.  16.18.  17.  6;  12;  30.  18.  48 ;  36 ;  84.  19.463  ft.  20.54. 
21.  48.     22.  8;  24. 

Page  110.    1.101;  207.     2.  1001;  5004.     3.2101.    4.3207.     5.3417. 

6.  4765.     7.  5555.     8.  6819.     9.  7890.     10.  9999.     11.  3333. 

Page  111.     1.  XV;  VIII;  XI;  XVII;  XIII;  IX;  V;  X;  XIV.    2.  11; 

9;  19;  14;  17;  7;  18. 

EP 


4  ESSENTIALS  OF  ARITHMETIC 

.  Page  113.  1.  $4.00;  $1.75.    2.  $16.00;  $3.03.    3.  $14.00;  $7.25. 
4.  $18.00;  $16.80.  5.  $230.00;  $175.75.  6.  $100.00;  $248.49.  7.  $184.00; 
$250.49.  8.  $200.00;  $500.50.  9.  $300.00;  $750.85.  10.  $400.00;  $286.98. 
11.  $768.00.  12.  $150.10.  13.  $275.10. 
Page  114.  1.  206.   2.  248.   3.  282.   4.  345.   5.  236.   6.  $238. 


7.  $160. 
Page  115.  1.  255.   2.  337.   3.  264. 

4. 

257. 

5. 

366. 

6.  3149. 

7.  3236.  8.  3704.  9.  4153.  10.  2503. 

Page  116.  1.  384.   2.  230.   3.  517. 

4. 

311. 

5. 

108. 

6.  $219, 

7.  $53.  8.  $300. 

Page  117.  1.  $560.  2.  680.  3.  703. 

4. 

615. 

5. 

$730. 

6.  $702. 

7.  800.   8.  766.   9.  888.   10.  $779. 

11. 

502. 

12. 

650. 

13.  462. 

14.  506.   15.  666.   16.  368.   17.  250. 

18. 

460. 

19, 

,  550. 

20.  517. 

21.  $736.  22.  $512.  23.  $515.  24.  $774.  25.  $718. 

Page  118.  1.  $10.47.  2.  $10.55.  3.  $8.65.  4.  $8.74.  5.  $14.70. 
6.  $5.39.  7.  $12.50.  8.  $15.70.  9.  $12.58.  10.  $12.35. 

Page  119.  1.  $4.11.  2.  $7.75.  3.  $6.15.  4.  $14.29.  5.  $10.72. 
6.  $7.29.  7.  $7.27.  8.  $4.69.  9.  $6.19.  10.  $5.77.  11.  $6.91.  12.  $5.21. 

Page  120.  1.  107.  2.  69.  3.  146.  4.  198.  5.  208.  6.  148.  7.  172. 
8.  118.  9.  189.  10.  99.  11.  323.  12.  70.  13.  429.  14.  203.  15.  565. 
16.  364.  17.  505.  18.  575.  19.  367.  20.  189.  21.  $148.  22.  $39. 
23.  $174.  24.  $41.  25.  $91.  26.  $125.  27.  $365.  28.  $108.  29.  $355. 
30.  $94.  31.  $114.  32.  $818.  33.  $99.  34.  $139.  35.  $85.  36.  $248. 
37.  $179.  38.  $48.  39.  $280.  40.  $578.  41.  $394.  42.  $379. 

Page  122.  1.  $47.49.  2.  $16.87.  3.  $17.78.  4.  $4.89.  5.  $29.92. 
6.  $5.45.  7.  $64.89.  8.  $28.92.  9.  $221.25.  10.  $171.25.  11.  $171.19. 
12.  $168.19. 

Page  123.  1.  $0.92.   2.  $78.49.   3.  $13.40.  4.  $8.73.   5.  $59.59. 

6.  $18.77.  7.  $8.89.  8.  $85.41.  9.  $24.13.  10.  $39.39.  11.  $9.69. 
12.  $17.64.  13.  $3.88.  14.  $34.25.  15.  $.53.73.  16.  $23.22.  17.  $15.39. 
18.  $12.57.  19.  $18.77.  20.  $74.31. 

Page  126.  1.  186.  2.  $1.26.  3.  $180."  4.  1206.  5.  1806.  6.  3006. 

7.  2406.  8.  5406.  9.  4206.  10.  33;  58;  40.  11.  48;  51;  20. 

Page  127.  1.  240.  2.  250.  3.  468.  4.  650.  5.  850.  6.  550.  7.  960. 

8.  963.  9.  975.  10.  1029.  11.  1338.  12.  1359.  13.  824.  14.  1080. 


ANSWERS  5 

15.  1590.  16.  1652.  17.  2608.  18.  4725.  19.  2030.  20.  2305.  21.  2080. 
22.  3262.  23.  4528.  24.  2184. 

Page. 128.  1.  8;  9;  10.  2.  9;  6;  7.  3.  4  ;  5;  11.  4.  5.  5.  6;  18;  5. 
Page  129.  1.  324.  2.  213.  3.  111.  4.  221.  5.  111.  6.  111.  7.  100. 

8.  224.  9.  423.  10.  231.  11.  112.  12.  212.  13.  110.  14.  110.  15.  100. 

16.  112.  17.  234.  18.  312.  19.  210.  20.  111.  21.  101.  22.  434.  23.  111. 
24.  111.  25.  120.  26.  102. 

Page  131.  1.  707.  2.  714.  3.  784.  4.  924.  5.  2345.  6.  1589. 
7.  1400.  8.  1428.  9.  1568.  10.  2268.  11.  2576.  12.  2534.  13.  2800. 
14.  2863.  15.  2933.  16.  3073.  17.  3423.  18.  6993. 

Page  132.  1.  8.  2.  5.  3.  7^.  4.  9^.  5.  $6. 

Page  133.  1.  52;  53;  54;  102.  2.  21.  3.  93.  4.  327.  5.  162.  6.  127. 
7.  121.  8.  81.  9.  97.  10.  62.  11.  145.  12.  73.  13.  57.  14.  101. 

Page  135.  1.  1600.  2.  1608.  3.  1616.  4.  1696.  5.  1936.  6.  2768. 
7.  2400.  8.  2880.  9.  2888.  10.  2920.  11.  3024.  12.  2664.  13.  3200. 
14.  3760.  15.  3800.  16.  3888.  17.  3984.  18.  2712.  19.  4600.  20.  4656. 
21.  5000.  22.  5400.  23.  5496.  24.  4572. 

Page  136.  1.  9;  10;  7.  2.  8;  9.  3.  8;  8;  16.  4.  16;  24;  32.  5.  8. 

6.  80.  7.  111.  8.  110.  9.  60.  10.  71.  11.  70.  12.  101. 
Page  137.  2.  $70;  |90;  |60.  3.  $72.  4.  72^. 

Page  138.  1.  2187.  2.  2880.  3.  3654.  4.  5148.  5.  7767.  6.  6678. 

7.  2946.  8.  4945.  9.  8181.  10.  5274.  11.  4295.  12.  4608.  13.  4104. 
14.  5274.  15.  2445.  16.  3234.  17.  5873.  18.  8847.  19.  47^. 

Page  139.  1.  6885.  2.  7218.  3.  6588.  4.  6102.  5.  4464.  6.  6183. 
7.  2412.  8.  2385.  9.  2655.  10.  2475.  11.  5283.  12.  6472.  13.  3591. 
14.  3357.  15.  3483.  16.  1854.  17.  2786.  18.  7024. 

Page  140.  1.  3.  2.  4.  3.  6.  4.  20.  5.  31.  6.  41.  7.  51.  8.  21. 

9.  60.  10.  40.  11.  50.  12.  100.  13.  110.  14.  111.  15.  101. 

Page  142.  4.  2;  3;  4;  5;  6;  7;  8;  9;  10. 

Page  143.  1.  2238.  2.  4145.  3.  5463.  4.  5352.  5.  3896.  6.  6881. 
7.  836.  8.  3612.  9.  4185.  10.  6084.  11.  2679.  12.  2862.  13.  5504. 
14.  3968.  15.  3123.  16.  3648.  17.  7497.  18.  5168. 

Page  145.  1.  50^;  $1.00.  2.  8;  80^.  3.  50f  4.  4^;  60f  5.  6^; 

18^;  90^.  6.  5pt. 


6  ESSENTIALS  OF  ARITHMETIC 

Page  146.  1.  6^;  9^.  2.  100^,  or  $1.  3.  180^,  or  $1.80.  4.  260^,  or 
$2.60.  5.  130^,  or  $1.30.  6.  70^.  7.  200^,  or  $2.  8.  120^,  or  $1.20. 
9.  700^,  or  $7.    10.  $2.50. 

Page  148.    3.  $460;  $1380. 

Page  149.    1.  6.    2.  16;  32;  32.    3.  2;  40. 

Page  150.  1.  15061b.  2.  1527  lb.  3.  13151b.  4.  12851b.  6.  7171b. 
6.  4451b.  7.  5721b.  8.  6741b. 

Page  151.  3.  6.  4.  70. 

Page  152.  1.  24sq.in.;  20  in.  2.  6  sq.  in.  3.  40  sq.ft.;  26  ft.  4.  36; 
24.  6.  J ;  4  sq.  in. ;  8  in. ;  16  sq.  in. ;  16  in. 

Page  153.  1.  $10.40.  2.  $20.20.  3.  $31.79.  4.  $108.61.  5.  $82.00. 
6.  $13.89.  7.  $27.30.  8.  $82.20.  9.  $219.00.  10.  $292.00. 

Page  154.  1.  54^;  57^.  2.  92^;  96f  3.  81^;  72^.  4.  75^;  69^. 

Page  155.  1.  $22.73.  2.  $15.87.  3.  $18.57.  4.  $212.86.  5.  $245.28. 
6.  $29.99.  7.  $26.42.  8.  $26.36.  9.  $70.75.  10.  $166.10.  11.  $2.96. 

12.  $3.76.  13.  $4.83.  14.  $1.86.  15.  $10.46.  16.  $3.89.  17.  $4.24. 
18.  $4.18.  19.  $24..58.  20.  $18.79.  21.  $3.09.  22.  $6.79.  23.  $3.21. 
24.  $22.89.  25.  $62.35.  26.  $2.58.  27.  $4.32.  28.  $1.73.  29.  $23.06. 
30.  $62.34. 

Page  156.  1.  $542.  2.  $1458.  3.  $2380.  4.  $3215.  5.  $4686 
6.  $5894.  7.  $7496.  8.  $2241.  9.  $2394.  10.  $6984.  11.  $5988.  12.  $5901 

13.  $5439.  14.  $3184.  15.  $7857.  16.  138;  174;  111;  189;  246;  264 
306;  102;  90;  171;  363;  207;  243;  249;  168;  285;  144;  480.  92;  116 
74;  126;  164;  176;  204;  68;  60;  114;  242;  138;  162;  166;  112;  190 
96;  320.  17.  70;  115;  140;  85;  205;  185;  245;  55;  120;  225;  125 
1.55.  56;  92;  112;  68;  164;  148;  196;  44;  96;  180;  100;  124.  18.  70 
91;  140;  147;  77;  84;  35;  42;  49;  56;  63;  154.  60;  78;  120;  126;  66 
72;  30;  36;  42;  48;  54;  132.  19.  90;  99;  45;  27;  36;  54;  63;  72;  81 
108;  117;  18.  80;  88;  40;  24;  32;  48;  56;  64;  72;  96;  104;  16. 

Page  157.  1.  70^;  74f  2.  48^;  56f  3.  96^;  92^.  4.  94^;  88^. 
5.  30^;  40f  6.  18^;  20^.  7.  72^;  76^.  8.  76^.  9.  71^. 

Page  158.  1.  5055;  1858;  7346;  1914.  2.  $1135.  3.  .5195.  4.  $1081.33. 
5.7678.  6.156.  7.  952  miles.  8.  $1.30.  9.  348^;  $3.48.  10.  $1161. 
11.  $405.  12.  2640.  13.  98f  14.  $2962.  15.  $385;  $405.  16.  $1944. 
17.  $47.  18.  $3384.  19.  $153.  20.  $3.83.  21.  256. 


ANSWERS 

Page  160.  1.  $9.89.  2.  $17.77.  3.  $27.82.  4.  $73.79.  5.  $172.82 
6.  $19.97.  7.  $34.54.  8.  $97.50.  9.  $95.65.  10.  $160.43.  11.  $29.03 
12.  $36.13.  13.  $100.66.  14.  $106.02.  15.  $104.01.  16.  $26.32.  17.  $31.60 
18.  $85.20.  19.  $109.71.  20.  $105.03.  21.  $2.42.  22.  $3.26.  23.  $3.33 
24.  $2.04.  25.  $8.55.  26.  $6.23.  27.  $4.38.  28.  $4.03.  29.  $5.64 
30.  $9.08.  31.  $5.64.  32.  $3.02.  33.  $6.78.  34.  $5.73.  35.  $8.89 
36.  $2.88.  37.  $3.89.  38.  $2.99.  39.  $5.29.  40.  $26.09.  41.  $339 
42.  $896.  43.  $2550.  44.  $9672.  45.  $9400.  46.  $6650.  47.  $.3495 
48.  $8163.  49.  $9024.  50.  $7000.  51.  $5400.  52.  $4963.  53.  $7308 
54.  $9450.  55.  $8550.  56.  234;  163;  228;  126,  rem.  1;  186;  107;  165 
rem.  1;  273,  rem.  1;  317;  209;  486;  452,  rem.  1.  57.  118;  148;  121 
rem.  2;  78,  rem.  1;  208;  217;  161,  rem.  1;  263,  rem.  1;  136;  297;  266 
325,  rem.  1.  58.  231;  188;  206;  228;  238,rem.3;  183,  rem.  2;  141;  180 
rem.  3;  148;  240,  rem.  1;  229,  rem.  2;  128,  rem.  1.  59.  102;  133;  104 
147;  128,  rem.  4;  112;  154;  177,  rem.  2;  118;  124,  rem.  3;  148,  rem.  2;  165 
60.  Ill;  104;  106;  120,  rem.  5  ;  122 ;  124,  rem.  2;  121,  rem.  1;  135;  137 
140,  rem.  5;  154;  155,  rem.  3.  61.  104;  106,  rem.  3;  112,  rem.  1;  113 
rem.  6;  116;  115;  123;  124,  rem.  5;  130;  133,  rem.  4;  134,  rem.  5 ;  135 
rem.  5.  62.  91;  93;  82;  84;  74;  64;  49;  38;  116;  123;  13,rem.  7;  27 
rem.  6.  63.  37;  74;  82;  73;  61;  36;  63;  45;  78  ;  89  ;  86,  rem.  3;  98,  rem.  6 

Page  164.  1.  19^.  2.  6^.  3.  32.  4.  160. 

Page  165.  1.  17f  2.  $12.25.  3.  $2.25.  4.  55f  5.  680.  6.  850; 
150.  7.  $1.30;  200.  8.  $3.50. 

Page  168.  1.  11.  2.  64.  3.  26.  4.  66.  5.  72.  6.  97.  7.  77.  8.  34. 
9.  XXXI.  10.  LXXXIX.  11.  XLII.  12.  XCI.  13.  LXVII.  14.  LXXV. 
15.CLXXV.  16.  CL.  17.MDCCCCXIX,orMCMXIX.  18.MDCCCCXX, 
or  MCMXX. 

Page  169.  1.  $9.14.  2.  $14.25.  3.  $14.20.  4.  $28.57.  5.  $42.09. 
6.  $34.61.  7.  $80.76.  8.  $86.16.  9.  $78.47.  10.  $75.48.  11.  936. 
12.  $920.30.     13.  21,451. 

Page  170.  1.  37  ft.  2.  77  men.  3.  453.  4.  278.  5.  149;  201.  6.  143; 
103.    7.  $.505.    8.  $438.    9.  21.    10.  716. 

Page  171.     1.  $140.40.    2.  $483.73.   3.  $190.70.  4.  $317.88.  5.  $294.98. 

6.  $320.26.    7.  $89.32.    8.  $123.14.    9.  $523.96.    10.  $221.88. 

Page  173.    1.  270.    2.  $2.70.    3.  550.    4.  $25.50.    5.  $40.80.    6.  $7.50. 

7.  $4.05.     8.  $21.75.    9.  $74.40.     10.  $101.50.     11.  $37.20.     12.  $35.80. 

EF 


8  ESSENTIALS  OF  AEITHMETIC 

13.  $11.65.  14.  $117.10.  15.  $148.20.  16.  $28.86.  17.  $24.54.  18.  $43.68. 
19.  $301.  20.  $183.75.  21.  $21.63.  22.  $25.13.  23.  $38.88.  24.  $575.44. 
25.  $298.68.  26.  $56.88.  27.  $19.17.  28.  $114.75.  29.  $132.75.  30.  $662.88. 
31.  $4.50.    32.  $22.75.    33.  $39.    34.  $58.80. 

Page  175.  1.  $27.50;  $127.50;  $227.50;  $255.  2.  $260;  $483 
$.532.50;  $697.30.  3.  $829.60;  $1000;  $2000;  $5000.  4.  840;  720 
1620  ;  1060  ;  1340.  5.  780  ;  $24  ;  $44  ;  $70  ;  $44.60.  6.  $90  ;  $114  ;  $98 
$155;  $193.  7.  400;  2200;  4500;  5000;  8100;  7500;  4200;  8600 
8.  7700;  3600;  8300;  8700;  6300;  6600;  2900;  9900.  9.  1000;  1600 
1400;  1800;  1200;  3000;  3600;  5000.  10.  7000;  8200;  9600;  11,000 
9200;  12,000;  13,400;  15,000.  11.  $60.  12.  $120.  13.  $250.  14.  $420. 
15.  $640.  16.  $1800.  17.  $70.  18.  $350.  19.  $682.50. 

Page  176.  1.  $3;  $3.60;  $4.20.  2.  $3.50;  $3.80;  $4.30.  3.  $2.40; 
$3.60.  4.  60f  5.  270;  270;  540.  6.  $3.50;  70^.  7.  $12.50;  $25;  $37.50. 
8.  $510;  $765.  9.  $1147.50;  $1530;  $2295.  10.  $5000;  $5625;  $4375. 

11.  $2275-  $910;  $1820.  12.  $3020;  $2642.50;  $1132.50.  13.  $1750; 
$2625. 

Page  177.  1.  $672;  $992.  2.  $903;  $1333;  $1763.  3.  966;  1113 
1365  ;  1596  ;  1743 ;  798 ;  1092  ;  1974  ;  1260.  4.  837 ;  1612  ;  2294  ;  1209 
2635;  1271;  868;  1953;  2976.  1107;  2132;  3034;  1599;  3485;  1681 
1148;  2583;  3936.  5.  1716;  2392;  2964;  2288;  1820;  3536;  2860 
4108  ;  4264.  2046  ;  2852  ;  3534  ;  2728  ;  2170 ;  4216  ;  3410 ;  4898  ;  5084 
2376;  3312;  4104;  3168;  2520;  4896;  3960;  5688;  5904.  6.  2444 
3588;  1300;  .3692;  4836;  1872;  4368;  3016;  4940.  2914;  4278;  1550 
4402;  5766;  2232;  5208;  3596;  5890.  3384;  4968;  1800;  5112;  6696 
2.592;  6048;  4176;  6840.  7.  5985;  5292;  7304;  9021.  8.  7104;  8232 
9306;  5632. 

Page  178.  1.  $72.30.  2.  $77.71.  3.  $106.78.  4.  $80.73.  5.  $.50.37. 
6.  $14.76.  7.  $69.44.  8.  $98.89.  9.  $172.80.  10.  $397.60.  11.  $202.74. 

12.  $110.88.  13.  $.54.21.  14.  $119.  15.  $66.75.  16.  $48;  $576.  17.  $12; 
$936;  $540.  18.  $84;  $175;  $266;  $322.  19.  $58.88.  20.  $109.48.  21 
22.  $141.45.  23.  $131.15.  24.  $337.50.  25.  $148.72.  26.  $231.  27, 

Page  179.  1.  $77.50.  2.  $80.30.  3.  $163.20.  4.  $220.50.  5.  $550. 
6.  $552.40.  7.  $101.20.  8.  $206.70.  9.  $213.12.  10.  $365.43.  11.  $880. 
12.  $1588.80.  13.  $435.  14.  $225.18.  15.  $420.  16.  $989.01.  17.  $.3993.40. 
18.  $8999.10.  19.  $918.75.  20.  $20,520.  21.  $13,608.  22.  $9351.70. 


ANSWEES  9 

23.  $5858.28.  24.  $29,898.81.  25.  $6868.80.  26.  $9140.60.  27.  $8447.60. 
28.  $11,244.22.    29.  $19,822.    30.  $48,007.20. 

Page  180.    1.  25,641.   2.  28,413.    3.  53,997.   4.  127,650.   5.  $185,150. 

6.  $195,800.   7.  30,618.   8.  83,868.   9.  139,167.    10.  75,828.    11.  $71,672. 

12.  $322,270. 

Page  181.  1.  $8840;  $9095;  $9265.  2.  $3825;  $.5362.50;  $4012.50; 
$4087.50.  3.  $50,044.80.  4.  $54,799.75.  5.  $69,501.78.  6.  $44,788.52. 

7.  $119,276.50.  8.  $187,360.56.  9.  $117,308.25.  10.  $165,232.78. 
11.  $286,144.20.  12.  $789,270.30. 

Page  182.  1.  $1.86.  2.  $1.26.  3.  $164.  4.  $1.26.  5.  $1.47.  6.  90f 
7.  90^.  8.  36f  9.  $1.80.  10.  $1.20.  11.  54f  12.  $1.08.  13.  $5.60. 
14.  $2.05.  15.  $1.89.  16.  $1.40.  17.  45^.  18.  $2.10.  19.  $1.80.  20.  $1.20. 
21.  $1.89.  22.  96f  23.  90^.  24.  $168.  25;  $1.20;  5^.  26.  84^;  16^. 
27.  46^;  4f  28.  $132;  $8.  29.  $350;  $50.  30.  $550;  $50.  31.  $590; 
$10.    32.  $155;  $5.    33.  $25;  $5. 

Page  183.   1.  5^.  2.72^;  3f  3.  $1.00.  4.  40^.  5.  60^.  6.  36^.  7.  $1.27. 

Page  184.    1.  24^.    2.  22 f    3.  60 f    4.  6f    5.  9^.    6.  12^.    7.  63 f 

Page  185.  1.  $4.85.  2.  $4.75.  3.  6.  4.  $189.75.  5.  58f  6.  $3.75. 
7.  $2.70.    8.  $38.50;  $77. 

Page  186.  1.  3552.  2.  3552.  3.  4984.  4.  64,296.  5.  85,869.  6.  37,093. 
7.  72,928.     8.  66,123.    9.  26,461.     10.  72,720.     11.  75,336.     12.  39,001. 

13.  64,218.  14.  677,329.  15.  96,933.  16.  90,873.  17.  282,492.  18.  390,656. 
19.  360,675.  20.  357,414.  21.  387,816.  22.  312,900.  23.  434,600.  24.  $51. 
25.  $190.56.  26.  $771.44.  27.  $605.64.  28.  $388.85.  29.  $592.02.  30.  $335. 
31.  $367.36.  32.  $498.96.  33.  $396.48.  34.  $473.04.  35.  $327.36. 
36.  $214.38.  37.  $235.17.  38.  $284.34.  39.  $711.75.  40.  $455.76. 
41.  $289.56.  42.  $657.72.  43.  $383.13.  44.  $307.80.  45.  $645.  46.  $821.30. 
47.  $367.36.  48.  $592.02.  49.  $1844.64.  50.  $967.98.  51.  $1444.85. 
52.  $1504.80.  53.  $1257.62.  54.  $1976.32.  55.  $4635.68.  56.  $2031.74. 
57.  $2621.88.  58.  $4174.08.  59.  $5236.59.  60.  $5077.26.  61.  $4016.04. 
62.  $2173.94.  63.  $3432.52.  64.  $6229.66.  65.  $6646.96.  66.  $2426.88. 
67.  $5308.82.    68.  $3684.20.    69.  $3410.68. 

Page  187.  1.  6;  7;  9;  13;  19;  27;  39.  2.  4;  8;  12;  13;  14;  15;  16. 
3.  17;  19;  21;  23;  24;  27;  32.  4.  12.  5.  14.  6.  15.  7.  6.  8.  12. 
9.  16.     10.  24.     11.  26.     12.  41.     13.  20.     14.  2.     15.  12. 


10  ESSENTIALS  OF  ARITHMETIC 

Page  188.     1.  914i.       2.  1043i        3.  1226i.      4.  706i.       5.  1170s 


6. 

321f 

7.  3601.       1 

S.  13741. 

9.  20581. 

10.  5841. 

11.  1698|-. 

12. 

2063f 

13.  1390|. 

14.  18561. 

15.  1170f 

16.  529|. 

17.  388f 

18. 

13071. 

19.  16412. 

20.  408f. 

21.  16205. 

22.  466^. 

23.  7182. 

24. 

1690f. 

25.  621f 

26.  1096f. 

27.  13061. 

28.  8233V 

29.  624^V 

30. 

918,V 

31.  298^8.. 

32.  3763^ig.. 

33.  376^V 

Page  191.  1.  11.  2.  12.  3.  13.  4.  111.  5.  112.  6.  141.  7.  121. 
8.  131.      9.  351.       10.  431.      11.  321.      12.  212.      13.  231.      14.  717. 

15.  155.     16.  65;  66;  76.     17.  22;  32;  33.     18.  581b. 

Page  193.  1.  23.  2.  45.  3.  25.  4.  116.  5.  133.  6.  16.  7.  23. 
8.  19.     9.  37.     10.  111.     11.  144.     12.  66.     13.  99.      14.  51.      15.  21. 

16.  24;  33.     17.  21;  31. 

Page  194.  1.  62.  2.  102.  3.  120.  4.  62.  5.  303.  6.  532.  7.  51. 
8.  64.    9.  402.    10.  111.    11.  102.    12.  102.    13.  222.    14.  109.    15.  107. 

Page  195.  1.  121.  2.  111.  3.  39^4^.  4.  58/^.  5.  5920.  6.  138ff 
7.  31ff  8.  88^.  9.  I6-5.V.  10.  139^2.  n.  4722.  12,  89|i.  13.  692|. 
14.  79f|.     15.  662T.     16.  85. 

Page  196.  1.  9.  2.  7.  3.  7.  4.  6.  5.  4.  6.  8.  7.  9.  8.  8.  9.  6. 
10.  7.  11.  8.  12.  8.  13.  7.  14.  9.  15.  8.  16.  66.  17.  88.  18.  82. 
19.  102,  rem.  1.  20.  81.  21.-  109,  rem.  3.  22.  112.  23.  71,  rem.  8. 
24.  66.  25.  77,  rem.  1.  26.  104.  27.  66.  28.  81,  rem.  5.  29.  113. 
30.  243.  31.  219,  rem.  3.  32.  91.  33.  73,  rem.  4.  34.  82.  35.  132. 
36.  123,  rem.  2.  37.  110,  rem.  8.  38.  51.  39.  71.  40.  87.  41.  29. 
42.  114.  43.  112.  44.  372.  45.  365.  46.  82.  47.  93.  48.  117lf. 
49.  11380.  50.  138^6^.  51.  141/j.  52.  2223.\.  53.  I7I21..  54.  85. 
55.  28.     56.  201^V     57.  141|f     58.  149|f.     59.  88f6.     60.  109ff 

Page  197.  1.  $4.5.  2.  $21.  3.35.  4.  $11.  5.  21;  22.  6.  43  mi. 
7.  46.      8.  $33.      9.  66.      10.  23;  $10.      11.  606.      12.  324.      13.  328. 

14.  792.     15.  1632.     16.  648.     iT  925.     18.  933.     19.  506. 

Page  198.     1.  $1.40.       2.  $0.54.        3.  $2.16.       4.  $2.88.        5.  $0.45. 

6.  $0.36.        7.  $0.36.        8.  $0.32.       9.  $2.70.        10.  $5.40.        11.  $0.27. 
12.  $0.48. 

Page  199.    1.  125.     2.  $2.50.     3.  $9.     4.  $0.16.     5.  $75.     6.  $850. 

7.  $3.80.      8.  32.      9.  6.      10.  32.      11.  4.      12.  24.      13.  30.      14.  49. 

15.  50.     16.  54.     17.  31<|.     18.  121.     19.  96.     20.  $1.40.     21.  $0.60. 
22.  447*^     23.  612^y     24.  810.     25.  964. 


ANSWERS 


11 


Page  202.  1.  8.  2.  34.  3.  10.  4.  13^.  5.  58^.  6.  21.  7.  47. 
8.  58§.     9.  7f.     10.  12.     11.  92.     12.  85^.     13.  82|.     14.  113§.      • 

Page  203.  1.  8§in.  2.  15^  in.  3.  5J.  4.2^.  5,  6§.  6.4^.  7.  12^. 
8.  17f  9.  3.  10.  4.  11.  6§.  12.  4§.  13.  7|.  14.  112.  15,  72. 
16.  7.     17.  6f.     18.  6|.     19.  12f.     20.  13f. 

Page  204.  1.  177;  118^.  2.  177;  117§.  3.  971^;  286.  4.  707|;  109. 
5.  557;  164.  6.  588^;  252f  7.  541^;  142^.  8.  557;  297§.  9.  456; 
197.  10.  849;  311§.  11.  730;  471^.  12.  778;  240§.  13.  631;  175§. 
14.  953i;  407^.  15.  1508;  411.  16.  1449;  352.  17.  975^;  424^ 
18.  896^;  303f.  19.  927§;  672^.  20.  834;  588§.  21.  469;  333|. 
22.  349;  251§.  23.  1010^;  811§.  24.  828^;  773^.  25.  1265;  376^. 
26.  1476;  437.  27.  1053;  564f  28.  993;  502^.  29.  1477;  178f. 
30.  999;  441|.  31.  927^;  275^.  32.  1367;  77§.  33.  1035|;  564^. 
34.  1104;  379.     35.  1123;  188^. 

Page  206.   2.  12.    3.  24.    4.  36.    5.  22.    6.  33.    7.  10.    8.  20.    9.  40. 

10.  66.    11.  100;  125;  150. 

Page  207.  .1.  6;  12;  7;  14 ;  20.  2.  4  ;  12;  8;  24 ;  30.  3.  5 ;  10 ;  15; 
30;  40.    4.  2;  10;  3;  15;  10.    5.  2;  6;  10;  10;  50. 

Page  208.  1.  42;  84.  2.  110;  220.  3.  150;  300.  4.  170;  340.  5.  213; 
426.     6.  241;  482.     7.  32;  96.     8.  56;  168.     9.  82;  246.     10.  86;  258. 

11.  131;  393.  12.  168;  504.  13.  45;  90.  14.  135;  180.  15.  67;  268. 
16.  290;  519.  17.  56;  280.  18.  121;  605.  19.  41;  123.  20.  205;  287. 
21.  180;  305.  22.  21;  242.  23.  123;  168.  24.  360;  400.  26.  39.  27.  18. 
28.  8  yd.    29.  287  ft.    30.  $450;  $270. 

Page  210.    1.  1.   2.  1.    3.  |.    4.  f    5.  1.   6.  If   7.  ^V    8.  f   9.  If 


13       ^5 

10.  ^g. 
I.    20.  11.    21.  1|.    22. 


10   1  1      1111      12   a' 

iU.      ly^.  li.     yj.  1-6.     ^^ 


14. 


18.  f     19 

27.  1|.    28.  2.    29.  2f.  30.  11.    31.  8. 


23. 


15.  U\ 


Iff- 


16.  f     17.  If 


24  I.    25.  14.    26.  1| 


■f 


"g- 


Page  211.  1.  4  yd.  2.  2  yd.  3.  3f.  4.  6|.  5.  3.  6.  6.  7.  11.  8.  4. 
9.  17f  10.  6.  11.  6f  12.  9.  13.  4f.  14.  14f  15.  5|.  16.  16|.  17.  lOf. 
18.  3|ft.  19.  3f  20.  8f.  21.  13|.  22.  lOjf  23.  12^V  24.  8^|.  25.  3f 
26.  lOf.   27.  14|.   28.  lOf    29.  11|.   30.  12.    31.  5f   32.  12f   33.  9f 


34.  14f    35.  9f    36. 


3f    37.  2f  in.    38.  10-|  in. 


Page  212.    1.  71  yd.    2.  7f  yd.    3.  4|.    4.  6f    5.  3f    6.  3|.    7.  If 
8.  14.    9.  U.    10.  3#. 


EP 


12  ESSENTIALS  OF  ARITHMETIC 

Page  214.  1.  300  qt.  2.  580  qt.  3.  24  qt.  4.  49  qt.  5.  700  qt.  6.  90  qt. 
7.  2qt.  8.  6qt.  9.  2  gal.  10.  9  gal.  11.  24  gal.  12.  12  gal.  13.  42  gal. 
14.  21  gal.  15.  60  gal.  16.  30  gal.  17.  16^;  4^;  32 f  18.  240;  480. 

19.  60^;  $2.40.  20.  8  da.  21.  150. 

Page  216.  1.  7;  1.  2.  14;  2.  3.  3;  14;  21.  4.  60;  1;  2.  5.  60;  1;  6. 

6.  120;  2;  10. 

Page  218.  1.  6156.  2.  32.  3.  $10,248.  4.  $63.  5.  $1200.  6.  54. 

7.  $89.60.  8.  6960.  9.  360.  10.  32.  11.  45. 

Page  219.  1.  7299.  2.  11,347.  3.  $6.61.  4.  $17.78.  5.  $43.53.  6.  10,691. 
7.  17,140.  8.  $10.85.  9.  $55.99.  10.  $95.24.  11.  266.  12.  2393.  13.  $4.66. 
14.  $4.87.  15.  $77.85.  16.  $46.75.   17.  $42.78.  18.  $605.76.  19.  $1531.60. 

20.  $5087.50.  21.  395/^-.  22.  578ff    23.  706f§.    24.  1925.   25.  1768f§. 

26.  51,984.  27.  166,772.   28.  365,211.  29.  639,576.  30.  43,681.  31.  108. 
32.  126.  33.  135.  34.  220.  35.  60.  36.  220.  37.  32  pt.  38.  64  qt.  39.  4  wk. 

Page  220.  1.  5i  hr.  2.  194 1  miles.  3.  $3.90.  4.  $1.05.  5.  5ihr. 
7.  61^.     8.  36^.    9.  63  f    10.  $2.25.    11.  $3.85.    12.  $24.60. 

Page  223.  1.  75,016.  2.  200,406.  3.  555,007.  4.  999,900.  5.  One 
hundred  twenty-five  thousand,  fifty.  6.  Three  hundred  four  thousand,  four. 
7.  Five  hundred  thousand,  five.  8.  One  hundred  one  thousand,  ten.  9.  One 
hundred  thousand,  one  hundred.  10.  One  hundred  twenty-three  thousand, 
four  hundred  fifty-six. 

Page  224.  1.  16,002,009.  2.  71,000,570.  3.  62,004,006.  4.  479,000,000. 
5.  515,000,300.    6.  6,093,017. 

Page  225.    1. 149,025  square  miles.  2.12,9001b.  3.  $786.08.  4.  $1081.74. 

5.  $2379.13.    6.  $856.34.  •       - 

Page  226.    1.  $456.03.  2.  $357.75.  3.  $417.02.  4.  $521.82.  5.  $505.39. 

6.  $108.35.    7.  $510.06.   8.  $400.65.   9.  $623.59.    10.  $97.77.    11.  $515.79. 
12.  $804.16. 

Page  227.  1.  $5346.  2.  $22,995.  3.  $25,110.  4.  $14,300.  5.  $30,070. 
6.  $26,508.  7.  $14,763.  8.  $20,444.  9.  $27,553.  10.  $58,420.  11.  $39,732. 
12.  $63,168.  13.  $79,985.  14.  $47,058.  15.  $50,594.  16.  $38,766. 
17.  $9072.  18.  $12,064.  19.  $16,875.  20.  $12,720.  21.  $46,272. 
22.  $28,875.      23.  $32,940.      24.  $22,101.      25.   $33,600.      26.  $11,368. 

27.  $19,992.     28.  $28,490.     29.  $19,136.     30.  $38,750. 


ANSWERS  13 

Page  228.  1.  15,640.   2.  106,875.   3.  54,954.   4.  131,588.   5.  251,560. 

6.  51,480.    7.  118,341.    8.  47,656.    9.  130,938.    10.  120,960.    11.  65,325. 

12.  75,296.  13.  197,640.       14.  498,381.       15.  571,356.       16.  126,766. 

17.  142,444.  18.  88,374.     19.  244,200.     20.  623,796.     21.  309,771. 

Page  229.     1.  55,937.   2.  36,663.   3.  190,454.   4.  159,075.   5.  440,450. 

6.  908,091.  7.  234,576.  8.  383,394.  9.  263,934.  10.  303,485.  11.  777,308. 
12.  564,682.  13.  263,250.  14.  598,850.  15.  1,180,912.  16.  807,216. 
17.  999,486.  18.  917,181.  19.  $28,125.  20.  $11,875.  21.  $1,194,875. 
22.  $853,200.  23.  $267.30.  24.  $312.80;  $340.  25.  $154,000;  $140,000. 
26.  $330,750;  $253,125.  27.  $8925;  $9409.50.  28.  $2875;  $2903.75; 
$3047.50;  $3105;  $3133.75.  29.  $8700;  $9004..50;  $9048;  $13,311; 
$13,441.50.   30.  $27,024;  $27,429.36;  $27,632.04;  $27,226.68;  $27,361.80. 

31.  $14,650;  $14,767.20;  $14,855.10;  $14,884.40;  $14,913.70.  32.  $21,150; 
$21,467.25;  $28,446.75;  $28,482;  $34,791.75. 

Page  230.    1.  20.   2.  205^^.   3.  201^}.   4.  200^^^.   5.  230^07.   e.  20. 

7.  20^«^.    8.  20^09.    9.  i7^y^T^.    10.  21^VVV 

Page  231.  1.  4.  2.  21.  3.  5.  4.  26.  5.  23.  6.  29.  7.  27.  8.  7.  9.  4. 
10.  6.    11.  7.    12.  41.    13.  6.    14.  34.    15.  33.    16.  24.    17.  22.    18.  8. 

Page  232.    1.  120.    2.  232.   3.  138.   4.  224.   5.  669.   6.  429.    7.  254. 

8.  206.  9.  532.  10.  413.  11.  380.  12.  461.  13.  342.  14.  352.  15.  378. 
16.  423.  17.  277.  18.  300.  19.  136.  20.  135.  21.  235.  22.  446.  23.  248. 
24.  124.  25.  312.  26.  138.  27.  253.  28.  309.  29.  338.  30.  348.   31.  425. 

32.  344.    33.  425.    34.  261.    35.  $353.    36.  $17.    37.  $35. 

Page  233.  1.  9;  108.  2.  2640;  1320;  660.  3.  160;  80;  40.  4.  36; 
198;  63,360.    5.  2;  17.    6.  264;  355. 

Page  234.    1.  224.   2.  6^2^.   3.  68.   4.  ^.   5.  112.   6.  7.   7.  832.  8.  22. 

Page  235.  1.  16;  16.  2.  240.  3.  1664  sq.ft.  4.  3654  sq. yd.  5.  1936  sq.ft. 
6.  703sq.yd.  7.  4214  sq.  ft.  8.  17,112  sq.  ft. 

Page  236.  4.  9  sq.  ft. ;  1  sq.  yd. ;  1296  sq.  in. 

Page  239.  1.  102  sq.  ft.  2.  324  sq.  ft.  3.  1113  sq.  in.  4.  300  sq.  yd. 
5.  1248  sq.  yd.  6.  1650  sq.  yd.  7.  1725  sq.  rd.  8.  1368  sq.  ft.  9.  1504  sq.  in. 
10.  5494  sq.  in.  11.  1551  sq.  yd.  12.  5184  sq.  ft.  13.  1102  sq.  in. 
14.  2666  sq.  mi.  17.  8  in.;  64.  18.  640.  19.  475.  20.  98. 

Page  240.  1.  38  ft.  3.  24  in. 


14  ESSENTIALS  OF  ARITHMETIC 

Page  242.  1.  3cu.ft.  2.  128cu.in.  3.  6.  4.  3192cu.m.  5.  37,lo2cu.in. 
6.  1656  cu.  ft.    7.  1396  cu.  yd. 

Page  243.     1.  1152.    2.  2160.    3.  180.    4.  192.    5.  2850.    6.  2310. 

Page  245.  1.  $216.75.  2.  $187.  3.  $6.10.  4.  $65.25.  5.  $92.75 ; 
$185.50;  $251.75;  $371;  $490.25;  $649.25.  6.  $80.75.  7.  $128.70; 
$137.80;  $150.80;  $162.50.    8.  $12.90.    9.  $12.90. 

Page  246.    1.  $24.75.    2.  $0.35.    3.  $1.85.    4.  $1.39. 
Page  247.    1.  $57.60;    $7.20;    $4.80.     2.  $10.81;    $86.48.     3.  $4.19. 
4.  $0.81.    5.  $3.92.    6.  $658.56.    7.  45  min.    8.  2  hr.  25  min. 

Page  250.     1.  15 ;  30.     2.  12 ;  60.     3.  27 ;  54.    4.  9 ;  18.    5.  15 ;  30. 

6.  21;  42.  7.  14;  28.  8.  18;  36.  9.  22;  44.  10.  13;  89;  52.  11.  6; 
18;  24.    12.  17;  51;  68.    13.  8;  24;  32.    14.  16;  48;  64.    15.  19;  57;  76. 

Paap  2.'i3      1     1-1-2.8.4.6.8.10     2     2.1.2.8.5.10.9.11 

3      4.2.6.8.12.28.1.2        ±        6    •      8.      9.      4.      8.      2.10..      1  K       1. 

^5  f;  i;  i;  f ;  f;  ^-  6.  f  in. ;  f  in. ;  ^  in.  is  the  greater.  7.  3*5  in. ;  ^\  in. ; 
^  in.  is  the  greater.     8.  f;f;f    9.  ^^5  ^5  1^5  tV?  iV    10-    A^A^^J 

12.  10.  9  11  8.  4.  14.  12.  6.  10  12  1-2..  8_  13  2.  4.  16 
IT'  IT'  T:J-      ^^-    17'  TS'  17'  17'  Iff'  17-  ^'^-   ^'  t'  16-  ^^'    IZ'  t'  Iff' 

14.  2;  2;  4.  15.  4;  4;  8.  16.  5;  5;  10. 
Page  254.  1.  |.   2.  l^.      3.  |.   4.  If   5.  If.   6.  If   7.  |. 

8.  If. 

Page  256.  1.  101b.  2.  5  yd.  3.  14|ft.  4.  24^  ft.  5.  87|:lb.  6.  57|. 

7.  341^  ft.  8.  222.  9.  552|  ft.  10.  ll^f 

Page  257.  1.  |  in.  2.  fin.  3.  |  in.  4.  f  5.  f  6.  |.  7.  ^.  8.  f 

9.  /^.  10.  f  11.  |.  12.  J^.  13.  ^V  14-  2,5^  in.  15.  2,V  16.  3f  yd. 
17.  4^  yd.  18.  4,Vm. 

Page  259.  1.  $4.  2.  $8.  3.  $28.  4.  $18.  5.  $32.  6.  $80.  7.  $125. 

8.  $84.  9.  $112.  10.  $222. 

Page  261.  1.  $7.17.  2.  $21.15.  3.  $13.04.  4.  $3.54.  5.  $1.63.  6.  $4.60. 
Page  263.  1.  $1.82.  2.  $2.93.  3.  $438.06.  4.  $197.98.  5.  $379.61. 

6.  $1030.60.  7.  $464.38.  8.  $355.85.  9.  $320.20. 

Page  264.  1.  $452.  2.  116.  3.  10^.  4.  $16;  $640.  5.  $29,080.  6.  55. 

7.  $365.  8.  $20.60.  9.  732.  10.  $117.50.  11.  378.  12.  $250.  13.  6. 
14.  $420.  15.  $2987.75.  16.  960  8q.rd.  17.  $1600.  18.  $1.  19.  5f 
20.  21.  21.  $6400.  22.  124;  31.  23.  128.  24.  80^.  25.  40^.  26.  $5.60. 


ANSWERS 


16 


5  in.  32.  36.  33.  12; 
38.  648;  45.36.  39.  72; 

$5.85. 

|3.70.  4.  20  f  6.  $1.75; 


27.  $4.80.  28.  20  yd.  29.  $90.  30.  160.  31. 
18;  48.  34.  52^.  35.  $3.75.  36.  54^.  37.  $8.70. 
144.  40.  45^.  41.  1^.  42.  65 f  43.  $10.  44. 

Page  269.  1.  $2.55;  $1.90.  2.  $4.45.  3. 
$1.75.  6.  25^.  7.  76.  8.  102. 

Page  270.  2.  98.  3.  $11.20.  4.  $11.90.  5.  $4.45;  $17.80.  6.  $2.95; 
$8.85.  9.  $47.84;  $5.98. 

Page  273.  1.  13,423.  2.  7860. 

6.  13,860.   7.  12,820.   8.  13,865. 
12.  16,298.  13.  17,074.  14.  13,008.  15.  8855. 
18.  13,420.  19.  13,829.  20.  7980.  21.  $101.19. 
24.  17,462.   25.  $174.62.   26.  $1746.20.   27. 
29.  $159.45.  30.  $136.46.  31.  1811.  32.  1976.  33.  2082.  34.  2219. 
35.  $13.98.  36.  $95.16.  37.  $61.50.  38.  $211.89.  39.  $95.88.  40.  $788.79. 

Page  274.  1.  3534.  2.  4238.  3.  1373.  4.  4121.  5.  3646.  6.  2307. 

7.  1869.  8.  6018.  9.  4909.  10.  1309.  11.  2471.  12.  1779. 
14.  3178.  15.  1848.  16.  194.  17.  2229.  18.  2799.  19.  589. 


3.  12,473. 
9.  18,371. 


4.  13,673. 
10.  7876. 
16.  7032. 
22.  $573.06. 

$142.58. 


5.  13,617. 

11.  16,224. 

17.  17,078. 

23.  10,119. 

28.  $128.24. 


21.  $26.12. 
26.  $344.26. 
31.  $102.23. 
36.  $124.09. 

Page  275 
7.  6510.  8. 


22.  $101.93. 

27.  $16.89. 

32.  $318.66. 
37.  $87.50. 

.  1.  1102.  2. 
7200.  9.  5848. 


14. 
20. 
25. 
30. 
35. 
40. 
45. 
50. 
55. 
60. 


34,868.  15.  58,176.  16 


56,196.  • 

454,658. 

207,792. 

552,234. 

259,956. 

$323.68. 

$647.68. 

$673.76. 

$8331.84. 

Page  276. 


21.  41,382. 

26.  824,588. 

31.  90,428. 

36.  358,080. 

41.  $97.44. 

46.  $709.38. 

51.  $41.70. 
56.  $1025.28. 


23.  $149.07. 
28.  $202.39. 
33.  $185.71. 
38.  $152.25.  39 

2940.  3.  6048. 

10.  3872.  11.  3304. 

.  73,704.  17.  43,522. 

22.  344,634.   23. 

27.  486,180.   28. 

32.  356,728. 

37.  345,040, 

42.  $290.40. 

47.  $408.48, 

52.  $96.88. 

57.  $3406.96, 


24.  $250.84. 
29.  $275.75. 

34.  $35.29. 

$517.40.  40 

4 


25 
30 
35 


13.  1017. 

20.  949. 

,  $271.66. 

,  $283.73. 
,  $272.34. 


$185.85. 


3780.  5.  928.  6.  8428. 
12.  13,287.  13.  49,989. 
18.  30,625.  19.  24,508. 


393,092. 

149,343. 

178,017. 

141,570. 

$203.75. 

48.  $691.18. 

53.  $229.04. 

58.  $5045.04. 


33. 
38. 
43. 


24.  210,384. 
29.  436,9.54. 

296,160. 

304,992. 

$2.54.94. 

$507.87. 
54.  $412.02. 
59.  $7009.08. 


34. 
39. 
44. 
49. 


7.  20U.  8.  26. 


1.16^1.  2.  15^.  3.  18|f.  4.20^1. 
10.  IS^a^.  11.  33f|.  12. 


5.  24M.  6.  164-J 


^7T 


Tff* 


9.  30/^. 


72|f  13.  196|f 


16  ESSENTIALS  OE  ARITHMETIC 

14.  221ff  15.  211|5.  16.  213/^.      17.  67fo.      18.  86 2|.  19.  106|^. 

20.  93^f  21.  51f^.  22.  66||.      23.  87ff.       24.  117ff  25.  88^|. 

26.  8628.  27.  724f.  28.  53^f.      29.  44^8..       30.  138|f  31.  66||. 

32.  98|f.  33.  77|f.  34.  54ff.  35.  43^V  36.  148f|.  37.  165^8. 
38.  89*9.  39,  67||.  40.  40fo.  41.  $12.  42.  $12.  43.  $4.32. 
44.  $144.  45.  $72.  46.  $121.  47.  $637.  48.  $202.  49.  $212. 
50.  $183.  51.  $105if  52.  $232^2^.  53.  $58|f.  54.  $671^.  55.  $113^. 
56.  $89|f.  57.  $69fT.  58.  $171^|.     59.  $167^|.     60.  $210^|. 

Page  277.    1.  f    2.  f     3.  f     4.  ^\.     5.  ^%.     6.  f     7.  f     8.  |. 

9.  10.  10.  ||.      11.  f      12.  f      13.  If      14.  If      15.  If      16.  f 

17.  If  18.  l^V      19.  l^f     20.  If     21.  f     22.  f     23.  f     24.  f 

25.  f  26.  f      27.  3-V      28.  ^V      29.  f      30.  ^\.      31.  f      32.  If 

33.  If  34.  2f  35.  H-  36.  ^\.  37.  2^V  38.  1^\.  39.  l^V 
40.  Iff  41.  214.  42.  276.  43.  416.  44.  156.  45.  552.  46.  121. 
47.  96.  48.  310.  49.  511.  50.  285.  51.  6f  52.  If  53.  7f  54.  f 
55.  9f  56.  4f     57.  5^f     58.  3^\.     59.  9if     60.  Oj\. 

Page  278.    1.  12  in.    2.  84  in.    3.  108  in.    4.  3  ft.    5.  21  ft.  6.  10^  ft. 

7.  36  in.  8.  90  in.  9.  16^  ft.  10.33  ft.  11.  5^  yd.  12.  49iyd.  13.  320rd. 
14.  1280  rd.       15.  1760  yd.       16.  880  yd.       17.  5280  ft.      18.  17,160  ft. 

19.  3520  ft.     20.  3960  ft.     21.  16  oz.     22.  12  oz.     23.  40  oz.  24.  lib. 

25.  91b.      26.  181b.      27.  20001b.      28.  70001b.      29.  2  pt.  30.  15  pt. 

31.  4  qt.  32.  15  qt.  33.  38  pt.  34.  4  pk.  35.  30  pk.  36.  8  qt.  37.  44  qt. 
38.  1008  sq.  in.     39.  63  sq.  ft.     40.  420  min. 


EP 


UNIVERSITY  OF  CALIFORNIA  AT  LOS  ANGELES 
THE  UNIVERSITY  LIBRARY 
Untf    ^h^  book  is  DUE  on  the  last  date  stamped  below 


JUL  1 
DEC  1  0  1951  i 

NOV  121959 


JAN  251988 
DEC  27^^^^ 


Form  L-> 
lOm-12, '39(3380) 


103 
W48 
V.l 


